Hasakah, Syria (CNN) Lightly armed, poorly equipped and exhausted by months under fire -- but determined to keep fighting: this is the reality of life on the front line against ISIS.

Rezan and his fellow soldiers are trying to stop the advance of some of the world's most feared terrorists, hiding out less than a mile away, across the plains of northern Syria.

They are the Kurdish YPG: proud and brave but an irregular force, scrappily clad in plaid shirts as well as camouflage gear, and armed with hunting rifles alongside their ancient AK-47s.

Theirs is no hi-tech war. The Kurds -- with just a few rocket-propelled grenades between them -- are trying to prevent ISIS from breaking through their lines.

"Of course we have mortars," one fighter told CNN, "but they are homemade."

There are no Humvees or armored cars here; the fighters are crammed into aging minibuses. To detect any ISIS movement, they have a cracked pair of binoculars.

Even their uniforms are ragtag -- in an extensive tour of frontline positions around the city of Hasakah, CNN met soldiers shod in socks and sandals rather than combat boots.

The United States is trying to help relieve the shortage of supplies. On October 11, more than 100 parachutes floated down through the night sky over northern Syria, each attached to a pallet of ammunition.

The airdrop was the first installment in a new U.S. strategy to help Syrian rebel groups after the failure of Washington's "train and equip" program.

But just who has the precious armaments remains a mystery.

While traveling through the region, a CNN team heard multiple accounts of who might have the ammunition, where it was being kept, and whether guns had also been dropped.

A Kurdish commander in the province of Hasakah confided to us that he knew where some of the supplies were, but smiled evasively when we asked to see them. Others said they'd been dropped to an Arab group or were in storage.

Wherever they are, the supplies (and many more like them) are badly needed if the new alliance -- known as the Syrian Democratic Forces -- is to go on the offensive against ISIS, as the United States hopes.

The YPG, a Kurdish group of some 30,000 fighters, is the senior partner in the Syrian Democratic Forces, which also includes some smaller Arab and Christian groups.

The Kurdish fighters say they are waiting for "zero hour" when they will advance south on two ISIS strongholds, Deir Ezzour and Raqqa, supported by coalition airpower.

There is no doubting the raw courage of YPG fighters, nor of the Kurdish Women's Defense Unit (YPJ) that fights alongside them. Flags and billboards carrying the pictures of Kurdish "martyrs" adorn the streets of every town in the region.

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But Raqqa and Deir Ezzour are essential to ISIS's "Caliphate" -- one as its heavily defended administrative headquarters, the other on a vital route into Iraq. Without much more help, there will be many more fading images of martyrs.

A few former soldiers from western countries fighting with the YPG told CNN that above all its fighters need tactical training.

"They throw themselves into battle, have no sense of covering fire, just charge at the enemy," said a Dutch veteran who is now a sniper with the YPG. "But they are unbelievably brave."

For now the front south of Hasakah is largely quiet -- the yellow-gray horizon shrouded in dust storms.

But ISIS is not gone; its fighters are lurking in villages on the road south to Deir Ezzour. They make probing attacks at night and run sleeper cells inside Hasakah -- anything to keep the YPG off balance.

Just weeks ago, a massive vehicle bomb blew up the entrance to the YPG headquarters here.

The Syrian chessboard

In the shadow of Jebl Abdelaziz, a mountain range that rises from the wide plains, are the charred ruins of an ISIS training camp.

Hidden from view among pine trees, its network of tunnels and trenches was still in place. Clips of ammunition rusted in abandoned vehicles. Our YPG guides warned us about the possibility of mines and booby traps.

At the gates, vehicles were peppered with shrapnel holes from an airstrike. The camp appears to have been occupied by an elite squad of suicide bombers, according to an ISIS video seen by CNN.

This corner of Syria is a religious and ethnic patchwork: Kurds, Assyrian Christians, different Arab tribes. They fight together and against each other.

Some Arab groups have thrown in their lot with the YPG, but around Hasakah there are villages known to sympathize with ISIS. In one, children yelled "God Bless Daesh" -- as ISIS is called here -- as our vehicles passed through.

Some Arabs in the countryside around Hasakah say they hated being ruled by ISIS.

Wadha, a grandmother surrounded by young children in dusty T-shirts and bare feet, said ISIS had beaten and killed people and forbidden her from smoking. They had taken the family's generator and water pump. Then airstrikes had destroyed houses across the road.

Now life is better, Wadha said, but all the time she glanced uneasily at the YPG fighters who had accompanied us into her village.

Other Arabs here resent that the Kurds were slow to join the insurgency against the regime, preferring to sit it out. Even now, the YPG co-exists with a substantial contingent of Syrian soldiers inside Hasakah city.

"We have nothing to do with them, though sometimes we have an agreement not to encroach on an area," Commander Lawand told CNN inside the YPG's bombed headquarters. "We are the real opposition to the regime, but first we must fight the terror groups."

That's just what the United States wants to hear. In the wake of its failed efforts to train and equip moderate rebel groups elsewhere in Syria, there is a lot riding on the Kurds and their Arab allies.

American airstrikes were instrumental in helping the Kurds save the city of Kobani on the Turkish border and then pushing ISIS back. In a country of shifting alliances, it's a proven partnership.

The Turkish question

But there's a problem: the Turkish government regards the YPG as a terrorist group because of its affiliation with Kurdish brethren in the PKK, which has waged an armed separatist campaign inside Turkey for 30 years.

Turkey is alarmed that the YPG now controls much of the Syrian border with Turkey and is essentially creating a state within a state, and may use newly supplied weapons to take over the last stretch of the border not yet under its control.

In a speech on Saturday, Turkish President Recep Tayyip Erdogan said: "All they want is to seize northern Syria entirely."

"We will under no circumstances allow northern Syria to become a victim of their scheming. Because this constitutes a threat for us," Erdogan said.

The flag of Rojava -- the name of Syrian Kurds' homeland -- flies everywhere. The Kurds have divided their land into three cantons. They are building checkpoints at the border with Iraq and even revising the school curriculum.

In battered cars and on café walls, the smiling moustachioed face of Abdullah Ocalan -- leader of the PKK -- peers down. His writings are absorbed by YPG fighters; some freely admit they have come from Turkey to lend experience to the YPG campaign.

The United States needs Turkey's help in the war against ISIS, so it has to tread carefully in helping the Syrian Kurds.

The Pentagon went out of its way to insist that the ammunition drop had gone exclusively to moderate Arab groups, (some of whom then said -- unhelpfully -- that they would share the crates with the YPG.)

Were the United States to begin supplying the Kurds with what they really need to take the war to ISIS, the reaction from Ankara would likely be incandescent.

And Erdogan is watching: "Whatever arms assistance they [the YPG] receive, it is coming from these countries. We know very well whose arms," he said.

Despite their lack of heavy weapons, the YPG can count on coalition airstrikes.

At his frontline position, Rezan clutched an orange GPS device. Marked up with coordinates, it helped his unit call in support from the skies.

He had spent seven days being trained to use it in the city of Qamishli. By whom? He raised his eyebrows and looked away.

"Believe me, I can't say," Rezan said sheepishly. "When you finish the training it's a secret. But they weren't speaking Kurdish."

The coalition carried out 140 airstrikes in and around Hasakah in August and September alone. Whole neighborhoods that were once occupied by ISIS are now a jumble of rubble and pancaked houses.

Commander Lawand says his men and women are ready to help Arab groups take Raqqa, and with western weapons "liberating the city will be quicker and easier."

Even so, he acknowledges that a force of some 20,000 will probably be needed to drive ISIS out of the jewel in its Syrian crown. There is no sense that an offensive is imminent.

"In the winter maybe," says Lawand, vaguely.

At some point in the distant future, the shape of a new Syria will have to be negotiated; until then, the Kurds are establishing "facts on the ground" to strengthen their bargaining position.

"Of course we are still Syrians," said one fighter resting on a sandbag outside Hasakah. "But first we are Kurds."