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

Let $H$ and $H^{\mathrm{\prime }}$ be two ample line bundles over a smooth projective surface $X$, and $M(H)$ (resp. $M(H^{\mathrm{\prime }})$) the coarse moduli scheme of $H$-semistable (resp. $H^{\mathrm{\prime }}$-semistable) sheaves of fixed type $(r,c_1,c_2)$. We construct a sequence of blowing-ups which describes how $M(H)$ differs from $M(H^{\mathrm{\prime }})$ not only when $r=2$ but also when $r$ is arbitrary. Means we here utilize are elementary transforms and the notion of a sheaf with flag.