Throughout the literature Wormholes are typically constructed by "Minkowski" or "Schwarzschild Surgery" (see e.g. Visser, Lorentzian Wormholes...), i.e. under quite simple and/or highly symmetric circumstances.
In the former case, regions are excised from a single manifold and their boundaries identified, and in the latter, two manifolds are joined.
In the Minkowski case, the joining is trivial (modulo orientational considerations) since the metric is constant (-1,1,1,1), and in the Schwarzschild case shell Jump Conditions (ref, Israel, Darmois, Lichnerowicz, O'Brien & Synge - of which I have only been able to track down a copy of Darmois online) are applied.
If one were to attempt similar surgery on a more general spacetime foliated by Cauchy hypersurfaces, adopting the approach that two regions are excised and identified on each slice, what conditions (metric, derivatives, etc.) should be imposed on the spacelike identifications within surfaces and what conditions on the timelike identifications between surfaces?