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I think I've heard "home and home" when it's a joint release, when a fan or a school, would say it solely from their perspective.  So I think a lot of times these announcement do call it a home and home series.  But as a fan youd say home and away.

This.
It's all about perspective. If you're a neutral party, it's a home and home. If you're viewing it from the perspective of one of the schools themselves, it's a home and away.

Yeah, it's just conventionalized. Bwarbs explained why, given the correct perspective, the convention makes sense, but the main code is both about the word used and how many times.
Neutral versus "home and home" is pretty obvious. Then there are pay-for-home games. Those are (perhaps) always scheduled as one-offs. We could call each a "home" series, but one event isn't a series, and this is never going to catch on. Still, it bears noticing that only "home and home" acknowledges two games, because (practically speaking) only series on each team's home turf are scheduled in increments greater than one. And that makes this home/away distinction nonsense. Doesn't matter. Identical info is there whether you call them home-and-homes, home-and-aways, or (Ick.) away-and-aways.

I presume we can presume any time two major programs announce a two game series, it is one game here and one game there, and a single game is played at some "neutral" site, like the Georgia Dome.

Which no longer exists.  I checked Stubhub for tickets to Saturday's Dawg game in Athens.  Good seats are about $50, which is a clue they are playing some opponent like say, UMass.  I might even go.  Tickets to the CG were running considerably higher.

Nobody says "away and away".

This really annoys me.

So what was it called when the Bearcats agreed to four road games @ OSU in exchange for one home game in the Bengals' stadium? 
Away, home, away, away and away? 

as long as we admit I am correct.....

I will admit that you're old

The NCAA should standardize this, heck, Congress should do it.

Would you rather have them do THIS or the other stuff they are apt to do?

Not meant to be political.  Sorry.