Martin's book is good, but necessarily brief on any particular topic because the scope of the work is huge. His section on the Neolithic is therefore very brief. Still, what he writes is that the old assumption, that Neolithic technologies spread from the Near East into Greece and beyond, is now more and more challenged as our chronologies are refined. What we find now is a lot of evidence in Greece (and Europe) that these technologies were in use in Greece/Europe as early as they were in the Near East. Transfer of Neolithic technologies took time, and so we must revise this idea that Tech A originated at Çatal Hüyük and then was carried by traders/refugees/whatever to other places, since now we can see that those technologies seem to be in use at roughly the same time in far-flung places. The technologies in question include agricultural techniques and crop types, animal husbandry techniques and types, basic copper metallurgical techniques, and monumental stone-shaping and stone-moving techniques.

Part of this is due to a long-standing discrepancy between Mediterranean and Near Eastern chronology. There was a gap there and the two sets of dates did not match up, but now that gap is closing thanks to improved modern techniques.