The camouflage-clad guerrilla, a Russian tricolour on his arm, heads one of two units tasked with flushing out government soldiers from a site at the heart of the six-month war, which has already claimed 3,700 lives.
Despite a five-week truce, his "Somali battalion" has been aiming tanks and rockets at Prokofiev International Airport, inflicting daily losses and reducing the futuristic structure to piles of rubble and twisted steel.
Ukrainian soldiers have been confined to the grounds' vast bunkers and other underground areas, giving the rebels de facto control, Givi boasts.
A thin man with sallow eyes and greying temples, Givi has turned into a star of recent battlefield dispatches.
He is a native of Abkhazia, which has similarly sought to break away from Georgia with Russian support.
In one separatist video, he calmly chats over a cigarette as a shell sends debris scattering next to him and other fighters run for cover.
Above ground, short-range rockets fly back and forth.
Some shells land a few metres from the building.
According to the gunmen, Ukrainian forces pound the city from outlying villages such as Peski, about two kilometers (1.3 miles) away.
"There are still soldiers underground, but we'll make them leave one by one. Every day we do some mopping up," he says.
"The airport is under our control."
Asked about the September 5 ceasefire agreement separatist leaders signed with Kiev under Russian pressure, Givi just gives a sarcastic smile.
"If there is an attack from them (Ukrainian soldiers), nobody will stop us -- neither the OSCE nor anybody else," he says in reference to the 80-strong team from the European security body monitoring compliance with the truce.
As has been the case throughout the uprising, sparked by the February ouster of a Russian-backed leadership, Kiev gives a completely different ground report, saying its troops have repelled the daily raids on the airport and maintained control.
Veteran of August bloodbath
Givi came to Donetsk with a group of separatist fighters, including a man named Motorola who leads another famed rebel unit, after they captured the eastern town of Ilovaysk in August.
Ukraine has confirmed it lost at least 100 soldiers in that battle.
Analysts believe the loss of Ilovaysk was so devastating and surprising that it convinced Ukrainian President Petro Poroshenko to sue for peace, and offer rebel-run parts of the east limited autonomy under the September ceasefire deal.
But Givi is only interested in total victory, with every last government soldier forced out of the Russian-speaking east.
"Together we will succeed," Givi says, leaning against a small sedan parked outside an apartment block taking over by the batallion, arms folded across his chest.
Behind him, a young man in fatigues too large for his frame and a toothless older fighter perch on empty mortar shell boxes, sipping artificial coffee and soaking in the autumn sun.
The rebels have taken over several upper floors of the building to give them a line of sight and fire on the airport.
Miraculously, several apartments are still occupied by their old residents.
On the fifth floor is the command centre used by Givi, who issues orders juggling a phone and a walkie-talkie while stepping over romance novels, tea boxes and other remnants of civilians' previous lives.
"We don't attack anyone, we merely respond to the fire," he says.
"We do this for the people who live around the airport so that they don't suffer Ukrainian shelling."
Source: Yahoo News