Assume $M$ a topological space,$f\in Homeo (M)$ then torus bundle $M_f=M\times I/\{(x,0)\sim (f(x),1)|x\in M\}$ obiviouly $f$ plays a significant role in determing the the torus bundle. hence there should be some general result of the following type: $M_f$ and $M_g$ are bundle isomorphic(resp.diffeomorphic) iff "W" here "W "is a relation between $f$ and $g$.

can someone help give W and explain?Thank you!