  We show that for every odd prime $q$, there exists an infinite family
$\{M_i\}_{i=1}^{\infty}$ 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.
