Assume that $K_{X}$ is semi-ample over $C$. If $\mathscr{X}$ is a good minimal $dlt$-model of $X$ and $\mathscr{Y}$ is any $dlt$-model of $X$, then $\mathrm{Sk}(\mathscr{X})$ is contained in $\mathrm{Sk}(\mathscr{Y})$. Moreover, $\mathrm{Sk}(\mathscr{X})$ can be obtained from $\mathrm{Sk}(\mathscr{Y})$ (as a topological subspace of $\mathrm{Sk}(\mathscr{Y})$ with piecewise affine structure) by a finite number of elementary collapses.