  Gay and Kirby introduced trisections which describe any closed oriented
smooth 4-manifold $X$ as a union of three four-dimensional handlebodies. A
trisection is encoded in a diagram, namely three collections of curves in a
closed oriented surface $\Sigma$, guiding the gluing of the handlebodies. Any
morphism $\varphi$ from $\pi_1(X)$ to a finitely generated free abelian group
induces a morphism on $\pi_1(\Sigma)$. We express the twisted homology and
Reidemeister torsion of $(X;\varphi)$ in terms of the first homology of
$(\Sigma;\varphi)$ and the three subspaces generated by the collections of
curves. We also express the intersection form of $(X;\varphi)$ in terms of the
intersection form of $(\Sigma;\varphi)$.
