Elementary transformations of toric vector bundles

We describe negative and positive elementary transformations of toric vector bundles in terms of Klyachko filtrations. We first determine the filtrations of the restriction of a toric vector bundle to an invariant prime divisor and then derive explicit formulas for the transformed bundle: only the filtration at the distinguished ray changes. As applications, we interpret adding and removing invariant boundary components of logarithmic tangent bundles as elementary transformations and recover the residue sequence for logarithmic cotangent bundles.