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

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