  We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy
loci of a map between vector bundles, under expected dimension conditions. This
result provides a unified way to understand known formulae for various
geometric situations such as blowups, Cayley's trick, projectivizations,
Grassmannian bundles, flops from Springer type resolutions, as well as provide
new phenomena such as formulae for Grassmannain type flips/flops and virtual
flips. We also give applications to blowups of determinantal ideals, moduli
spaces of linear series on curves, and Hilbert schemes of points on surfaces.
