  Let $K$ be a non-trivial knot in $S^3$, and let $r$ and $r'$ be two distinct
rational numbers of same sign, allowing $r$ to be infinite; we prove that there
is no orientation-preserving homeomorphism between the manifolds $S^3_r(K)$ and
$S^3_{r'}(K)$. We further generalize this uniqueness result to knots in
arbitrary integral homology L-spaces.
