Let $X$ be a projective Calabi-Yau variety over $K$. Then the essential skeleton $\mathrm{Sk}(X)$ is a strong deformation retract of $X^{\mathrm{an}}$. If $\mathscr{X}$ is a good minimal dlt-model that satisfies the assumption in (2), then $\rho_{\mathscr{X}}$ is homotopic to the identity on $X^{\mathrm{an}}$ relative to $\mathrm{Sk}(X)$.