Avdiivka, Ukraine - Svetlana Zadorozhnyuk crunches through the new snow towards the evacuation bus, holding the hand of her 10-year-old daughter. This is the second time she has sent her little girl away from the fighting in eastern Ukraine, but that has not made it any easier.

"I'm just so tired of all this," she says through a tear-choked voice.

The girl has spent her days sitting next to her mother as she tended shop, terrorised by the sound of the incoming and outgoing artillery that has killed around two dozen and wounded many more on both sides of the frontline around the town of Avdiivka since hostilities spiked in the area on January 29.

The fighting, which seems to have eased a bit in the past days, is among the worst escalations since the Minsk II ceasefire agreement was signed in February 2015. Some here speculate that the surge in violence is connected to the inauguration of Donald Trump as US president - as a way for Russian President Vladimir Putin to test Trump's intentions over the war in Ukraine.

Regardless of the causes, Svetlana has had enough. She gives the girl's name to the organisers of the evacuation, who check it against their list of children. Then, her daughter is motioned on board.

The girl waves to her mother through the glass, breathes on the window and writes, "I love you" in the fog. "The situation now is just terrible, terrible. Right now no one knows what will happen in the next five minutes," says Svetlana.

As the driver idles the engine in the -10 degrees Celcius temperatures, 76-year-old pensioner Valentina Fyodorovna stands on the other side of the bus and tearfully looks up at her baby grandson. The blue-eyed boy bounces on his mother's lap as they wait to drive to Sviatohirsk, a pilgrimage town that is now serving as a temporary home to thousands of internally displaced people.

"I would give my pension. I would give anything for this to stop," says Valentina, wiping away her tears. The randomness of the shelling means she and everyone else in Avdiivka fear that they will not live through the night.

READ MORE: Losing everything in Avdiivka

Saving the children

For the past week, Avdiivka, an embattled industrial town on the frontline in the war in Ukraine, has struggled with freezing temperatures, intermittent heating, and no power or water.

Now that the shelling is subsiding and the power is coming back on, the people of the town are taking stock of their ordeal and speculating on the causes of last Sunday's sudden shift from a frequently broken ceasefire to outright shelling and fighting.

The gathered mothers wave to their children as the bus pulls out. Artillery continues to rumble and thump intermittently in the background. An organiser says 23 were leaving that morning and that slightly fewer than 200 children had left by the service since last Sunday.

More had fled with their families, though schools in the town continued to hold classes.

This crisis is only the most recent since the war broke out in 2014, after pro-Western protesters deposed the pro-Russian president. Soon after, Russia annexed Ukraine's Crimean Peninsula, the site of a large Russian naval base. Kiev and the West say the Kremlin then fomented and backed a rebellion in the east of the country, while Russia says it was not involved.

READ MORE: Dam leaves Crimea population in chronic water shortage

The Donald Trump factor

Just across the street from where the bus was parked, Mikhail Kolodych, sweeps glass and splintered wood from his sister-in-law's kitchen floor.

A shell had hit the building the night before, destroying the apartment on the floor above and shattering all the windows in this one. Everyone was already sheltering in the basement of the building - as they have been since 2014 - so no one was hurt.

In the kitchen, a shell fragment is lodged in the wall. Surveying the destruction, Mikhail echoes the sentiments of Valentina, the pensioner at the bus stop, visible through the shattered window.

"Russia is unpredictable. They have awoken and wherever they turn tomorrow, they can go. Even to the Baltic states - Estonia, Latvia, it is possible," he says.

"I think the situation is connected with President Trump," he says, warning that if Trump and other world leaders do not strengthen sanctions, "[the conflict] will grow - just look at Syria".

So far, he has seen little from the international community to make him think they will do more to help halt the fighting. But a big problem is that Trump is "also unpredictable", he says, but adds, "I think he can't just wake up and go do whatever he likes. It's not like in Russia."

On Saturday, Trump called Ukrainian President Petro Poroshenko, the first direct contact between the two leaders since Trump was sworn in on January 20. Trump's stated aim of improving relations with the Kremlin has sparked fears in Kiev that the US may lift sanctions against Russia, levied against the country for its annexation of Crimea and support of rebels in the breakaway regions of Donetsk and Lugansk.

"We will work with Ukraine, Russia, and all other parties involved to help them restore peace along the border," Trump said in a White House statement, after talking to the Ukrainian president. Poroshenko's office said the call with Trump particularly focused on the "settlement of the situation in the Donbass and achieving peace via political and diplomatic means" and that the two sides "discussed strengthening the strategic partnership" between the two countries.

Trump told Fox News host Bill O'Reilly on Saturday that, "I respect a lot of people, but that doesn't mean I'm going to get along with [Putin]. He's a leader of his country. I say it's better to get along with Russia than not."

On Sunday, Vice President Mike Pence responded to the upsurge in fighting on ABC's This Week news programme, saying, "We're watching and [are] very troubled by the increased hostilities." But, when questioned on sanctions continuing against Russia, he said, "That's a question that will be answered in the months ahead." That response that will do little to allay fears in Kiev.

Indeed, many in Avdiivka believe that last week's upsurge in violence was a direct result of Putin wanting to test Trump's mettle.

"Maybe it is that before they meet, they needed to feel each other out," says Dmytro Linko, a member of the Ukrainian parliament who was in Avdiivka observing the army.

OPINION: Ukraine as testing ground for Kremlin-Trump 'dialogue'

Stocking up on emergency supplies

Down the street from Mikhail's sister-in-law's wrecked apartment, volunteers and Ukrainian emergency crews swarm around School Number 2.

Outside the front door, a mortar had blasted frozen earth across the front yard, leaving a dark pit and a broken tree. The volunteers unload truck after truck packed with bottled water, candles, blankets, food, diapers and other humanitarian aid donated by international and Ukrainian organisations.

Even with the sound of shelling a near constant in the background, hundreds of people gather to collect what they can.

One young mother is intent on picking up candles, since her two young sons are as terrified of the dark as they are of the shelling.

"There was shelling today and my youngest slept through it," she says, rocking her stroller back and forth in the crowd outside the school. But the older one, she says, "understands and feels everything. When the shells started to fall he got frightened. His heart, I don't know, must have been beating 300 times a second."

Now, she is standing in line to pick up some candles, "so that he is not afraid during the attacks and not scared of the dark".

Gallery