At the moment, the rebels are within reach of surrounding a contingent of hundreds of Ukrainian troops dug into the town of Debaltseve, a crucial rail hub. “We are on the move and they are trapped,” Batya said.

His fighters are deployed on the edge of the strategic city of Horlivka, not far from the only road still connecting Debaltseve — 23 miles to the east — with Ukrainian-controlled territory to the north. The road has come under regular fire in recent days and is sometimes impassable.

The grand house where Batya and his troops make their headquarters used to belong to a regional prosecutor. But he fled in the face of the separatist advance, so now the rebels are lords of the manor. The soaring, two-story entryway, wrapped in a grand wooden staircase, is now the company canteen, a pot of bubbling stew perfuming the air, boxes of medical supplies stacked in the corner.

Batya makes his office in a front parlor, chattering on walkie-talkies with his troops while his top fighters smoke cigarettes on a sofa and flick ashes into a shell casing.

“This is our famous fighter,” he said, laughing happily and gesturing to a small woman seated beside the window. Her name is Ira, and before the war she was the secretary at a kindergarten in Shakhtarsk, a town several miles to the south. Batya is from the same town, as are most of his fighters — outside of a couple who described themselves as volunteers from Russia.

“She is known as 01,” he said, pronouncing it “zero one,” which is an emergency telephone number, like 911 in America. “She goes into the field to rescue our fighters when they are wounded. Plus she is our best sniper. She can cook for us. She can drive our tank.”