\begin{tikzcd}[row sep=scriptsize, column sep=scriptsize] & f^* E_V \arrow[dl] \arrow[rr] \arrow[dd] & & E_V \arrow[dl] \arrow[dd] \\ f^* E \arrow[rr, crossing over] \arrow[dd] & & E \\ & U \arrow[dl] \arrow[rr] & & V \arrow[dl] \\ M \arrow[rr] & & N \arrow[from=uu, crossing over]\\ \end{tikzcd}