The Wikipedia article for the Danube civilization is replete with references for how the Danube civilization of the Neolithic and Chalcolithic-era (i.e. copper metallurgy) Balkan peninsula is the direct ancestor of Minoan civilization of Crete, Cycladic civilization, and Helladic civilization, including its last phase, Mycenaean Greece. It goes as far as to call them the "offspring" of the older Danube civilization.
However, this Google Books search yields basically no information on this supposed linear relationship between the Old Europe or Danube civilization and the subsequent Cycladic, Helladic, Mycenaean, and Minoan civilizations of the Aegean Sea. I've also found little to nothing in the scholarly journal database JSTOR about this proposed relationship.
The Danube civilization, for reasons of agricultural and natural disasters plus the invasions of the Indo-Europeans, was already well into decline by the end of the 4th millennium BC (c. 3000 BC). In fact, the Greeks themselves were Indo-European newcomers to southeastern Europe. If the Mycenaean Greeks and Minoans of Crete were influenced at all by the Danube civilization, or more specifically the Cucuteni-Trypillian and Varna cultures, to what extent has that been proven? What hard evidence in artwork, architecture, ceramic pottery, metal tools, etc. shows a direct link between these civilizations? Or is the Wikipedia article that I've shared simply full of hot air? I haven't been able to check the sources used for that article, so I'm not sure which credible academics support this theory.