I need help with my homework problem.
For a fibration $$F \to \mathcal{E} \xrightarrow{p} B$$
prove that the transgression $\tau: E^{0, m-1}_m \to E^{m, 0}_m$ coincides with the composition
$$E^{0, m-1}_m \hookrightarrow H^{m-1}(F) \xrightarrow{\delta} H^m(\mathcal{E}, F) \xrightarrow{(p^{*})^{-1}} H^m(B, pt) \cong H^m(B) \twoheadrightarrow E^{m, 0}_m.$$
I have seen a proof of a similar result on homology but couldn't adapt it.