To define Seiberg-Witten invariants one needs homology orientation. So for a closed oriented smooth (let us say as well simply connected) 4-manifold $M$, a homology orientation is an orientation of $H_2(M;\mathbb{R})$.
I read that for example knot surgery (where $K$ is a knot and $T^2$ an embedded torus of self-intersection $0$ and where $\varphi:\partial (T^2\times D^2)\to \partial (S^1\times (S^3\setminus K))$ maps $\{\mathrm{pt.} \}\times \partial D^2$ to a longitude of $K$)
$X_K:=\big(X\setminus (T^2\times D^2)\big)\cup_{\varphi}\big(S^1\times (S^3\setminus K)\big)$
induces a homology orientation on $X_K$. How does the transfer of homology orientation work?
I could imagine that this is not complicated, but I do not know how one can describe this precisely.