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Let $H$ and $H'$ be two ample line bundles over a smooth projective surface$X$, and $M(H)$ (resp. $M(H')$) the coarse moduli scheme of $H$-semistable(resp. $H'$-semistable) sheaves of fixed type $(r,c_1,c_2)$. We construct asequence of blowing-ups which describes how $M(H)$ differs from $M(H')$ notonly when $r=2$ but also when $r$ is arbitrary. Means we here utilize areelementary transforms and the notion of a sheaf with flag.

Blowing-ups describing the polarization change of moduli schemes of semistable sheaves of general rank