Is the Asian portion of Azerbaijan and Georgia south of the caucasus mountains? And is Cyprus entirely in Asia?
I can answer this in two ways, If you are looking at this from a plate tectonic perspective then Cyprus is part of the Anatolian plate which is mostly Turkey with little bits of the countries to the north of Turkey. To the east of the Anatolian plate is the Arabian plate which is NOT considered as part of Asia. The Eurasian Plate comprises most of Europe and much of Asia including Azerbaijan and Georgia. But these are west of the Ural Mts and in the mountains pushed up as the Arabian plate has pushed into this area. Thus technically on the European side of the Eurasian plate.
The second is from a geopolitical way of looking at things. Turkey is considered Asia Minor along with Northern parts of the Middle East. Cyprus is considered by some to be part of Europe and by others as part of the Middle East. Depending on who you speak to on the island they also have a difference of opinion. Azerbaijan and Georgia are Asia Minor as they reside in the Caucasus Mts. The Urals Mts are the dividing line between "European and Asian" Russia.
I"m not sure if this helps or has caused more confusion.