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.
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