Kirby in this paper claims (page 4) that "... any two h-cobordisms between $M_0$ and $M_1$ are diffeomorphic" citing two papers of Kreck. In the latter of these papers the main result is the following:
Theorem: Let $M_0$ and $M_1$ be fixed closed oriented smooth $1$-connected $4$-manifolds. Then the set of diffeomorphism classes rel. boundary of smooth $h$-cobordisms between $M_0$ and $M_1$ is isomorphic to the set of isometries between the intersection forms of $M_0$ and $M_1$.
I do not see how Kirby's claim at all follows from this, it actually seems to be explicitly in contradiction to the cited theorem. What am I missing?
Edit: I dug up the other reference of Kreck ("Ist 4 Denn Noch Normal?" where Kreck says that the above result (evidently) implies that fixing an isometry between the intersection forms of $M_0$ and $M_1$ fixes a unique $h$-cobordism between these manifolds, so that is the likely referent here. Then my question becomes why we get for free in our setup an isometry between the intersection forms of $M_0$ and $M_1$.
