Infinite homotopy stable class for 4-manifolds with boundary

We show that for every odd prime $q$, there exists an infinite family $\{M_i{\}}_{i=1}^{\mathrm{\infty }}$ of topological 4-manifolds that are all stably homeomorphic to one another, all the manifolds $M_i$ have isometric rank one equivariant intersection pairings and boundary L(2q, 1) # (S^1 \times S^2), but they are pairwise not homotopy equivalent via any homotopy equivalence that restricts to a homotopy equivalence of the boundary.