Let $X$ be a $\mathbb{Q}$-factorial, normal variety and $(X,\Delta)$ has KLT singularities.
Let $f: X \to Y$ be a $K_X + \Delta$-flipping contraction and $f^+: X^+ \to Y$ be its flip. I was wondering if the exceptional loci of $f, f^+$ maps to the same variety? That is to say whether $$f(Ex(f)) = f^+(Ex(f^+))?$$
This is true in the toric case because the image of both loci can be express explicitly in the same combinatoric data. However, I was unable to show it in the general situation.