For a second, I thought... (Spoilers)

Nothing transfers from game to game. If you have clear data saved and load up the next game, it'll give you a bonus (swimsuit and some extra skill points in Ep. II, and Shion's Vector uniform in Ep. III). That's it though. Nothing to really worry about.

While Episode I does continue straight into Episode II, Episode III does not. The time between the end of Episode II and beginning of Episode III is totally missing, and condensed into a bunch of database entries you read at the beginning of the game. Not only that, but even though Episode III wraps up the story arc decently, there was much more planned for the series that never materialized, and it shows. So the series basically does wind up ending on a cliffhanger but with some sense of closure.

What we basically got was the first half of the first third of the series (Episodes I and II), and the last fourth of the second half of the first arc (Episode III), while missing the first part of the second half of the first arc and completely missing the last two story arcs (four more episodes -- confused yet?). Development was hell, sales were bad, and the publisher kept cutting their budget until they gave up. It's a shame, really, as Xenosaga was by far the best RPG series from the PS2 era onward, even if it wasn't quite as good as Xenogears.