  In this article, we study the variation of the Gieseker and Uhlenbeck
compactifications of the moduli spaces of Mumford-Takemoto stable vector
bundles of rank 2 by changing polarizations. Some {\it canonical} rational
morphisms among the Gieseker compactifications are proved to exist and their
fibers are studied. As a consequence of studying the morphisms from the
Gieseker compactifications to the Uhlebeck compactifications, we show that
there is an everywhere-defined {\it canonical} algebraic map between two
adjacent Uhlenbeck compactifications which restricts to the identity on some
Zariski open subset.
