Each time a body arrives, Anatoly Turevich opens a file on his computer and adds to his list. Often the only detail he is able to add is "man" or "woman". There are 511 entries. Turevich, the 62-year-old director of Luhansk's main morgue, has seen a lot in his three decades of work, but the past few months have been more grisly even than the mining accidents he was used to.

Luhansk, a town of more than 400,000 inhabitants, has been the worst-hit city in east Ukraine during the recent conflict. Capital of the self-proclaimed Luhansk People's Republic, the city spent more than a month encircled by Ukrainian forces. As battles raged between local rebels, with Russian support, and the Ukrainian army and volunteer battalions, more than half the city fled, to relatives in other cities or refugee camps in Russia. Those who stayed were generally those too frail to move or those with absolutely nowhere to go.

Turevich picks a number at random, launching a series of photographs of blackened remains that bear only a passing resemblance to the human form. Relatives of the missing can flick through the gruesome catalogue and see if they recognise their loved ones. If a body is too disfigured for photographic identification, the morgue has taken DNA samples, though it has no ability to analyse them. At some point in the future, they will be sent somewhere that does, Turevich hopes.

Of the seven specialists at the morgue, five left when the fighting started, while the sixth drove over a mine on his way to work, and is now in hospital. That left Turevich to handle the influx of corpses on his own.

"I could have left, but then who would do this work?" he asks, before cutting the interview short. A van carrying 15 decaying bodies has just arrived. They have been dead for weeks, but the roads were far too dangerous for their relatives to transport them. The list will now total 526. Turevich says the vast majority are civilians, and almost all have died from shrapnel wounds.

After a fragile ceasefire between Ukrainian and rebel forces agreed last week, people are finally able to bring out their dead. Turevich expects many more busy days in the near future.

In the courtyard, more than 50 wooden coffins are neatly stacked under a cloud of flies. All are full; sometimes a chunk of yellowed torso or bloodied clothing is visible through the gap between lid and casket. A generator now works intermittently, keeping the bodies inside the morgue partially refrigerated. For much of August there was no power at all. "People think we must get used to the smell," says Turevich, whose office is also infested with flies. "You never get used to the smell."

Post-apocalyptic

The ceasefire agreed a week ago has meant the shelling has ceased for the first time in two months. A semblance of normality is returning to the city. At its vast locomotive factory, closed after shells landed inside its territory, there is hope that work might start up again as early as Monday. In the basement training room, which has served as a makeshift bomb shelter for more than 100 people, only five were left on Wednesday, the rest having returned home as the explosions finally stopped.

But there is a long way to go. Luhansk has a post-apocalyptic feel, as people stumble into the brightness from the bomb shelters, and thousands of those who left arrive back on buses, their possessions bundled into large bags. There are few cars, as petrol is scarce, so many people are on bicycles or trudging long distances on foot.

Lyubov Zheleznyak near a house cellar where a brother and sister, Vitaly and Marina Yushko, burned to death in early August. Photograph: Maria Turchenkova

There has been no water or electricity in the city for more than a month. Almost every cafe and restaurant has been shuttered for weeks. At the few open stalls, people wait in snaking bread queues for the first time in two decades. They draw water from wells; on street corners generators are hooked up to a spaghetti of wires from which mobile phones can be charged. To actually make a call, they have to find one of the few isolatedspots on the city outskirts where one bar of reception is available. There, dozens of people gather waving their phones in the air as if in a bizarre ritual, hoping to get a signal and finally make contact with relatives who worry they may be dead.

In the suburb of Yubileynoe, 90 residential apartment blocks suffered some kind of damage in recent months, while 16 took direct hits. It is unclear who will pay for the huge structural repair work required. The residents certainly cannot afford it, the local rebel government has not offered, and Kiev has no control over the territory. Their best hope for now appears to be a volunteer group using equipment from the local coal mine.

"The aim of the Ukrainian army was to destroy everything, so that people would be on their knees and beg to be allowed to return to the fascist Ukrainian state," says 47-year-old Vyacheslav Pleskach, a rights activist who is now volunteering to help those whose houses were damaged in Yubileynoe. "There was nothing of military value here at all, nothing. They were just shelling the most vulnerable people, day and night."

Others note that the rebels would often wheel artillery to positions in residential areas, fire at Ukrainian positions outside the town, and speed off. By the time the return fire came, the rebels were long gone and civilian homes suffered. Viktor, who sent his wife to Kiev but refused to leave the flat in central Luhansk he had worked so hard to buy, claims often the rebels themselves would fire at residential areas.

"Once there was just a few seconds between the outgoing sound of mortar fire and the explosion," he says, from the small candlelit apartment he could not bear to leave. "It came from very close. It had to come from within the city, which means the rebels."

Amid the passions, rumours and disinformation, understanding who shot where and when is extremely difficult. But there seems little doubt that both sides are responsible for civilian casualties, and by firing on civilian areas, Ukrainian forces have made any eventual process of reintegration even harder, as anger grows.

Viktor in the apartment in Luhansk he refused to leave. Photograph: Maria Turchenkova

In the suburb of Bolshaya Verkhunka, the devastation is absolute. After a battle in early August, the Ukrainian National Guard took up a position on one side of the suburb; the rebels were on the other. Each side relentlessly attacked the other, over the heads of the residents. Almost every house on the main street is destroyed.

In the house 65-year-old Nikolai Zapasny built with his own hands between 1975 and 1981, some of the walls are missing, much of the roof has gone, and all the windows broken. The interiors, painstakingly decorated in a chintzy manner unthinkably luxurious for such a locale, have been destroyed by shrapnel; the walls turned into Swiss cheese. "I always wanted these sofas. Look how nice they were, and now look at them," says his wife, tearfully. "We hadn't even paid off the loan."

His beloved car, a sky-blue Volga 21, kept in mint condition for three decades, is now a tangle of gnarled metal; even his bicycle is destroyed. For two months, he and his wife have been cowering in a dank basement as the house above them was slowly pulverised. "Both sides were shooting, all the time. Nobody from either side ever came in to ask us who was living here. They would have found no bandits, just old people." Zapasny's wife sobs uncontrollably, while he simply stares into the middle distance, unable to comprehend how his entire life's work has been shot to pieces.

"We don't care what country we live in. We just want them to stop killing us," says their 58-year-old neighbour Lyubov Zheleznyak, a widow. Her house was relatively unscathed, but is still riddled with bullets and all her windows are blown out. Pensions have not been paid for months; she has no money for food, let alone repair works.

Further down the road, Vitaly and Marina Yushko, a brother and sister both in their early 30s, were hiding from the shelling in their cellar in early August when the house took a direct hit. Rubble fell over the entrance to the cellar, jamming it shut, while flames engulfed the remains of the house. Unable to escape, the pair burned to death.

It was not possible to move the bodies because of the constant fire, so the neighbours buried the charred remains of Vitaly and Marina in a shallow grave in their back garden. Nobody informed the authorities, as there was no way to make contact with them, a sign that the real death toll could be much higher than the numbers given at the morgue.

After a sustained battle a week ago, the National Guard fled the area, part of a broad and bloody Ukrainian retreat Kiev says was spurred by the rebels gaining an injection of Russian firepower. Evidence of the retreat is visible on the roads out of Luhansk. Burnt-out armoured personnel carriers and tanks stand at regular intervals on the road. At Lutuhyne, more than 20 vehicles were incinerated by artillery and Grad rockets, their twisted and blackened remains now picked over by children scavenging for scrap metal.

Nikita, 10, plays with a burned rifle at a site where a Ukrainian military convoy was destroyed. Photograph: Maria Turchenkova

'Our hearts ache with despair'

Nobody in Luhansk knows what the future holds. Many people do not want to talk about politics. Nobody knows whether in six months' time they will be part of Ukraine or part of a breakaway state, and there could be recriminations for calling it the wrong way and backing one side. Meanwhile, people try as hard as possible to pretend that everything is fine.

"Parents see the schools opening, and it gives them the impression that everything is all right; it helps them," says Valentina Kiyashko, the city's director of education, an imposing yet kindly matriarch with a shock of peroxide hair and an implacable manner. "I behave as if everything is normal because people know me and they like to see that everything is fine. But of course inside it's hard. Everything feels constantly shaken up."

She herself has been sleeping on the floor of the bathroom or in the entrance hall to her flat; as has her 86-year-old mother. Several times shells landed in the courtyard of her apartment block.

Of more than 60 schools in Luhansk, only six have opened. Some have been severely damaged, in others there are simply no children as they have all been evacuated. All the teachers who were asked to report for the new school year have done so, despite the fact that none have received a salary for the past three months.

At an annual competition for singing, dancing and painting among the city's different schools, the turnout is less than a quarter of last year's, but everyone is determined to put on a show despite the circumstances. A dance ensemble is decked out in matching blue uniforms; a young girl with her hair tied in ribbons valiantly battles her way through a violin sonata.

Pupils from different schools at a singing and dancing competition in Luhansk. Photograph: Maria Turchenkova

The festivities are interrupted by a poem written and performed by the adult son of the headmistress, stanzas of shrieked anguish and raw emotion about hearing a Grad rocket attack, the imprecise launchers that hail down up to 40 rockets in one salvo.

"Our hearts ache with despair … There is no earth, there is no sky … Grad! Grad! Grad!"

The children look on in shock while most of the teachers are choked with tears.

In Luhansk, emotions are never far beneath the surface. A teacher begins sobbing at the question of whether the region should stay part of Ukraine or separate; another cannot bear to talk about one of her students, whose parents drove over a mine in their car. His mother died instantly; the child's legs were blown off and he later died in hospital.

In a scruffy field not far from the morgue, there are mounds of freshly dug black earth, dozens of simple wooden crosses with plyboard signs; names and dates of birth scrawled in black marker. Protective gloves and masks, worn by the gravediggers, are discarded in the grass. The lonely silence is broken periodically by low booms from the airport; rebels exploding ordnance left behind by the Ukrainian army when they fled.

There are men, women, pensioners, children. Many simply have "unknown" and a number; some day perhaps relatives will recognise a body on Turevich's list and match it with the number on the grave. A huge, open trench is partially filled with coffins; a dozen of them arranged in a neat line. There is space for many more.