On the Fiber Homotopy Equivalence of Two Fibrations

Given two fibrations P:E → B and P' : E' → B with the same fiber F_bo at b_o ∈ B one constructs two associated fibrations NPe_o → F_bo and NP'e_o → F_bo, e_o ∈ F_bo, and show that, under some connectivity assumptions on the spaces concerned a homeomorphism g : F_bo → F_bo induces a fiber homotopy equivalence between [NPe_o]_g and NP'g(e_o).