Let $f:X\dashrightarrow Y$ be a birational map of smooth projective varieties.
Is known that if $f$ is a small modification then $h^0(f_*(D))=h^0(D)$ for any divisor $D$ of X.

Exists a relation between $h^0(D)$ and  $h^0(f_*(D))$ in general for a divisor $D$ of X?