I'm anthropologist, not a historian, but I think concepts of belief systems 'transitioning' from one thing to another is a little out of date and out of favour, and ultimately must be based on a good deal of speculation, as much of it occurs in unwritten portions of history. Any claims in this regard are up for debate, and probably differ on a case by case basis. For instance there are other ways in which pantheons of gods could conceivably arise from local guardian spirits, and tribes or villages joining together etc.
As far as animism vs theism goes (of anybody's interested), one of my favourite ethnographies is Hugh Brody's Other Side of Eden. He compares the creation stories of arctic hunter-gatherer tribes with that of Genesis, and makes a strong case for the Judeo-Christian belief system being one of agriculturalists - of dominating nature, rather than forming relationships with it. Indeed, when you read much of it back it makes a lot of sense
; e.g. all that going forth and multiplying is a good strategy for agricultural societies, but a bad one for those living in a hunter-gatherer system.