Homotopy-equivalent not implies homeomorphic for compact connected orientable 3-manifolds

Statement
It is possible to find two fact about::compact connected orientable manifolds $$M_1$$ and $$M_2$$, both of dimension 3, such that $$M_1$$ and $$M_2$$ are both fact about::homotopy-equivalent spaces but are not fact about::homeomorphic spaces.

Proof
Consider the three-dimensional lens spaces $$L(7,1)$$ and $$L(7,2)$$. These are homotopy-equivalent but not homeomorphic.