It is 100%-pure pseudo-science, but Bear does a careful job of making it pseudo-science which doesn't contradict what we know. (Too much.) (For example, there is no FTL-travel through ordinary space.)
General Relativity tells us that spacetime is an active thing which interacts with the rest of the universe and changes through those interactions, not a passive background or a sort of theater in which things happen. It also makes it clear that spacetime need not be topologically simple like the Euclidean space of Newtonian physics. It can be very, very complicated and twisted and interconnected and still be a perfectly good spacetime obeying General Relativity.
This all naturally leads to the possibility that a sufficiently advanced technology might be able to manipulate spacetime like we manipulate steel, and that's what we see in Eon and its sequels.
Bear's pseudo-science also obeys Clarke's Law and for our purposes might as well be magic. While we can't say that the twisted spacetimes of Eon are impossible, we can't say anything meaningful about how to bring them about, either, (other than that it would take a really, really, really lot of energy.)
The part that struck me as most unrealistic is that these contorted bits of spacetime don't produce extreme gravitational effects in their vicinity. GR suggests that the curvatures that appear to be present in Eon would manifest as really, really, really extreme gravitational fields.
But SF usually needs some sort of escape from science-as-we-know-it, and a novel that involves super-science even moreso. I think Bear did a fine job of writing realistically about very unrealistic science!
