Are different lifts of a homotopy in a Serre fibration vertically homotopic? – mathoverflow.net

Let $p:E \to B$ a Serre fibration and a homotopy $H:X \times I \to B$ with the initialization $X \times 0 \mapsto \tilde{h}_0$. Let $\tilde{H}_1$ and $\tilde{H}_2$ two different lifts of $H$. Are ...