It is claim in the book "Higer-Dimensional Algebraic Geometry" by Olivier Debarre (before Theorem 7.21 page 183) that
If $D$ is a divisor with simple normal crossing on $X$ and $\pi: Y \to X$ is a birational projective morphism whose exceptional locus has simple normal crossing, $\pi^*D$ still has simple normal crossings.
I feel this claim is skeptical (maybe think of $Y$ as a blow up of some variety $B$, and $D$ is tangent to $B$?). My question is this a true statement? Or the author apparently means other thing?