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Given a Poincaré-duality space X much information can be gathered from its GW-theory. As GW-theory is generally hard to compute, one important question is how GW-theory behaves under gluing of spaces. In this talk I will present a criterion which guarantees a splitting of the GW-theory of a pushout in a part fitting in a Mayer-Vietoris sequence and an error term. The criterion applies more generally for localising invariants and allows generalizations of splitting theorems of Waldhausen and Cappell for the K- and L-theory of certain pushout rings.