probably with a lot of animosity if not outright violence, I'd think! My headcanon is that Eve and Leviathan have sort of settled into their territories in Purgatory; Eve rules the lands and forests and everyone who scurries on the surface, and Leviathan rule the skies and seas, both of which are of course littered with border skirmishes and such and so on.
Purgatory being mostly strife to begin with, it's probably not hard for either side to come up with a reason to pick a fight, but I'd imagine from the way the vampire Alpha interacted with Edgar, most of the invading is on the Leviathan's part. A Leviathan raiding party can be fended off with some well-placed beheadings, but even on hostile soil that's more like a temporary setback than a real loss for them. Even the big dogs wouldn't challenge a Leviathan in their own territory without a damn good reason.