Let $Y, Y_0, Y_1$ be homology 3-spheres (over $\mathbb Z$).
Fact (Poincaré-Perelman) : if $\pi_1(Y)=1$, then $Y$ is homeomorphic to $S^3$.
Question : does $\pi_1(Y_0)=\pi_1(Y_1)$ implies $Y_0$ homeomorphic to $Y_1$ ?
If not, do you have a counter-example ?