  Given a family of Calabi-Yau varieties over the punctured disc or over the
field of Laurent series, we show that, after a finite base change, the family
can be exended across the origin while keeping the canonical class trivial.
More generally, we prove similar extension results for families whose
log-canonical class is semi-ample. We use these to show that the Berkovich and
essential skeleta agree for smooth varieties over ${\mathbb C}((t))$ with
semi-ample canonical class.
