The term people's republic does not reflect Marxist socialism. Instead it is representative, as the New Republic as pointed out, of a very old school of Russian conservatism which connects Eastern Orthodoxy and societal collectivism of a Christian socialist variety.
Here is a quick guide:
Donetsk People's Republic
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Located in Donetsk Oblast, this was the first "people's republic" to declare independence from Kyiv. Most of the fighting has been done in Donetsk.
Luhansk People's Republic
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Located in Luhansk, this people's republic has been slower in forming but picked up speed as Kyiv focused most of its "anti-terrorist" operations in Donetsk.
Federal State of New Russia aka Novorossiya
It is unclear whether or not The Federal State of New Russia, also known as Novorossiya, exists. The leadership of the Donetsk People's Republic all states it does but the leadership of the Luhansk People's Republic is divided on whether or not they belong to it. This implies Novorossiya may be an effort by the more successful Donetsk People's Republic to control Luhansk People's Republic.
While some have noted the flag of Novorossiya mirrors the Confederate battle flag, this is a concidence. Red, white, and blue are the colors of Russia and the Novorossiya flag is almost a dead copy of the Russian naval jack.
Odessa People's Republic
Declared on the internet to the shock of anti-Kyiv protesters in Odessa, this people's republic seems to exist online only.
Kharkiv People's Republic
Crushed within one day of its founding.
The only "real" people's republics are in Donetsk and Luhansk. While these claim their respective oblasts, their real control is demonstrated in the map below showing where Ukrainian elections were unable to be held.
|Grey shows areas of no voting, i.e. people's republic hold on territory.|