(CNN) Wrapped in a blanket and wearing pink sandals, a little girl sobs in fear as she walks down the street, gunfire blasting at the end of the road.

Confused, she turns around and covers her face with the blanket.

At that moment, a soldier from Iraq's elite special forces the Golden Brigade rushes forward to help -- "don't cry," he says, as he guides her to safer ground.

The girl—who looks little more than 10 —is followed by her younger sister and mother, who also holds a baby in her arms. The family is one of many fleeing this neighborhood in eastern Mosul as the Golden Brigade fights street by street, house by house, to drive out ISIS.

An Iraqi soldier tells people to gather for aid distribution on December 8.

As the battle for Mosul enters its third month, the Iraqi military's rapid advances over open territory in the initial weeks have been replaced by a slow, hard slog.

Iraqi forces have so far managed to drive the terror group out of 30% of the city and officials are no longer predicting an end to ISIS by the end of the year.

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This has been a battle hard fought, in which Iraqi troops must painstakingly go through each house to make sure danger does not lie within. Awaiting them could be an ambush, explosive, or anxious family huddled inside.

Their task is further complicated by the presence of hundreds of thousands of civilians still in the city.

In the weeks before the offensive began in mid-October, the Iraqi army dropped millions of leaflets over Mosul urging residents not to flee their homes if they felt safe, to cooperate with pro-government forces and to provide information via a toll-free telephone number.

Tens of thousands did flee -- but many more have stayed in their homes.

A soldier from the Mosul Brigade of the Iraqi forces operates a drone on December 5.

One young man shares with an Iraqi commander the footage he shot on his cell phone of ISIS positions in his street. The commander -- who gives his name only as "Mohammed"-- then calls in the coordinates.

Moments later, Mohammed says his men "killed one Da'ish" -- using the common term for ISIS. "Now the situation is good," he adds.

A warm welcome?

Residents of eastern Mosul appear to have welcomed government forces, greeting them with kisses and embraces.

One young man even prepared a poem for their arrival, full of praise for the army and curses for ISIS.

Meanwhile, bicycle repairman Yasir has a more nuanced view of life under ISIS rule.

"Life was normal," he says. "They imposed upon us how we should shave, how we should dress. If you conformed it was fine, but if you didn't they whipped you."

"I'm not afraid of the army and I wasn't afraid of ISIS. Both have laws. If you follow them you won't have any problems -- 50% of the people in Mosul don't have a problem with ISIS," he added.

The unravelling of ISIS

ISIS was able to seize control of Mosul in June 2014 in a matter of hours from a much larger government force, aided and initially applauded by many residents who were weary of the heavy-handed Baghdad government.

But support for ISIS eroded as its draconian rule sank in. The group dished out harsh punishments for minor infringements such as smoking, seized the property of minorities, and destroyed ancient sites and monuments.

In the end ISIS could promise little other than endless war against the world, a harsh life of ideological purity and complete isolation, and a world view focused on the apocalypse.

What they left behind

Among the houses in one east Mosul neighborhood, Iraqi troops discover a training center for fighters, the walls covered in diagrams of assault rifles and hand grenades.

Most of the recruits "were between the ages of 12 and 14," explains an officer.

Loaves of bread are still on the counter in the kitchen. They must have left in a hurry.

Iraqi soldiers eat in a house in the Entisar neighborhood of Mosul last month.

For now, the authorities are struggling to provide the basics. One health care center is up and running, but it's not enough says its doctor Abdallah Ismail.

"We have many patients with renal failure, chronic disease, Leukemia -- and we have no hospital for treatment of such cases," he said.

On the outskirts of the city the relief effort is ongoing. Workers hand out crates filled with bottles of water and plastic bags with essential items such as food, blankets and clothing.

A displaced Iraqi man and child ask for help as a British charity distributes food on December 4.

"I am from Mosul, I'm Christian," says one volunteer Ma'an 'Ajaj . "I decided to help my friends, my brothers from Mosul after Da'ish leave it."

He hands a crate of water to a young child who responds with a smile before walking away arms filled with about a dozen bottles.

The process of healing in Mosul could take a very long time -- but there is hope.