We follow [BFJ16, Definition 1.1] and say that a regular scheme ${\mathscr{X}}$ of finite type over $K^{\circ}$ is SNC if its special fiber has simple normal crossing support and if any intersection of irreducible components of the special fiber is irreducible. As noted in the remark after [BFJ16, Definition 1.1], if ${\mathscr{X}}$ is strictly semi-stable [dJ96, Definition 2.16], ${\mathscr{X}}$ might not satisfy the second condition, however, a vertical blowing-up of ${\mathscr{X}}$ along non-connected components of such intersections will be SNC.