The changing fortunes of war in northern Iraq are recorded in layers of graffiti daubed on the walls of villages overrun by Islamic State militants this summer, but since re-appropriated by Kurdish peshmerga forces.

"Bravo peshmerga," read the freshest markings, painted over older inscriptions - some of them already scribbled out - that proclaim "property of the Islamic State".

Village by village, Kurdish forces have regained around half the territory they gave up in August when IS militants tore through their defenses in the northwest, prompting September's airstrikes by the United States - their first since 2011.

The Kurds scored a particularly important victory recently, driving Islamic State fighters from the strategic Rabia border crossing and severing their main artery from Mosul to Syria, which had been used to re-supply fighters on both sides.

Though their brethren in Syria have lost control of hundreds of villages to IS fighters, prompting thousands of refugees to flee to Turkey, the Kurds in Iraq now feel as though the tide has turned in their favour.

But to secure the rest of what they have lost they will now have to overcome numerous challenges ranging from a lack of heavy weaponry and US air support in eastern areas close to Iran's border, to hostile residents rejecting their claim in other areas.

MINES AND TANKS

Peshmerga secretary-general Jabbar Yawar illustrates the problems along the front line by tracing it across a map with his laser pen: from Rabia on the Syrian border in the northwest to Khanaqin near the Iranian frontier.

"Our plan is to liberate the areas we lost," he said, and explained how next his men will wait for Iraqi forces to liberate the northern province of Salahuddin and western Anbar governorate before the next push after that.

"We can't advance on Mosul on our own. If they (Iraqi forces) get close to Nineveh, we can carry out joint operations."

Northeast of Mosul, IS militants are still in control of the Nineveh plains, home to religious and ethnic minorities that fled en masse when the peshmerga pulled out in August.

The Kurds have since re-captured all the high ground surrounding the plains, giving them a strategic advantage.

But they say the flat terrain below would be tough to defend without tanks and armoured vehicles - though Western allies sent arms, the Kurds report that what they received is no match for Islamic State's arsenal, which includes U.S.-made Hummers plundered from the Iraqi army.

Further progress has also been complicated by improvised explosive devices planted by IS as it retreated - the peshmerga have taken control in more than one town only to relinquish it again because of mines and counter-attacks by suicide bombers.

Yawar said a decision had been made several weeks ago to halt advances on some fronts in order to limit casualties until the peshmerga received bomb detectors and robots from Western countries, as well as instruction in how to use them.

Britain has sent some and is training peshmerga at a base in the Kurdish city of Suleimaniyah.

A PATCHWORK OF ALLIES

When the Iraqi army abandoned its bases in the north, the Kurds moved forward to realise long-held ambitions in the disputed territories - then found them less easy to retain.

Wary of overextending themselves again, they now show little interest in venturing into areas where they are likely to encounter resistance from the local population: In the Makhmour area south of Arbil, for example, fighting has lulled for several weeks, but the peshmerga are in no hurry to risk a backlash from Arab residents that resent their takeover.

"You need an Arab force there because of the ethnic sensitivity,"said Kurdish official Nejat Ali Saleh in Makhmour.

It is not clear what Arab force could be enlisted to help, but U.S. and Iraqi officials plan to incorporate Sunnis into a "National Guard" force to decentralise power from Baghdad and turn them against Islamic State.

South of Kirkuk, Kurdish forces have found an unlikely Arab ally in Shi'ite militia which have rallied to fight IS in the absence of an army. Together the forces have driven militants back from the town of Tuz Khurmato and last month broke a long siege of Amerli nearby.

Elsewhere the Kurds are working closely with the Iraqi army, particularly on the eastern part of the frontline.

Forces belonging to the Patriotic Union of Kurdistan's party are the main presence between Kirkuk and the eastern city of Jalawla, not far from the Iranian frontier. But the United States and their allies have bombed no further east than Amerli - because, say some Kurdish officials, that would bring their planes uncomfortably close to Iranian airspace.

However the Iraqi army still has a presence in the eastern Diyala province that also homes Jalawla, and its planes are conducting strikes in the area.

Yawar said Jalawla - which has changed hands several times since the IS militants initially surged through Iraq - was almost entirely encircled by peshmerga, which are now waiting for Iraqi forces to take the city of Tikrit in the neighbouring province of Salahuddin.

"We expect that if this area is liberated by the Iraqi army the supply route will be cut...and...they will leave the area." - Reuters