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

Statement

It is possible to find two Compact connected orientable manifold (?)s $M_{1}$ and $M_{2}$, both of dimension 3, such that $M_{1}$ and $M_{2}$ are both Homotopy-equivalent spaces (?) but are not Homeomorphic spaces (?).

Proof

Further information: three-dimensional lens space

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