Lemma: A crepant birational map between quasi-projective normal varieties with only terminal singularities is in fact small modifitacions, i.e. isomorphism in codimension 1.

So, if $f:X\dashrightarrow Y$ is a crepant birational map of smooth varieties and $p\in X$ a point, then $f|_{X-\{p\}} : X-\{ p\} \dashrightarrow Y-\{ f(p)\}$ is a crepant birational map between quasi-projective smooth varieties so is a small modification by the lemma above and then $f$ is a small modification.

Is it right or im missing something?