Kirby's generalized Property R conjecture

Let $Y$ be an integer homology sphere containing a knot $K$ which admits a surgery to $S^1 \times S^2$. Kirby's generalized Property R conjecture. Then $K$ is unique up to ambient diffeomorphism. This is an analogue for integer homology spheres of Gabai's Property R theorem for knots in $S^3$. The conjecture is disproved by the exotic Mazur manifolds constructed in the paper, whose inequivalent smooth structures give inequivalent belt spheres.