  We prove an equivalence between the Bryan--Steinberg theory of $\pi$-stable
pairs on $Y = \mathcal{A}_{m-1} \times \mathbb{C}$ and the theory of quasimaps
to $X = \mathrm{Hilb}(\mathcal{A}_{m-1})$, in the form of an equality of
K-theoretic equivariant vertices. In particular, the combinatorics of both
vertices are described explicitly via box counting. Then we apply the
equivalence to study the implications for sheaf-counting theories on $Y$
arising from 3d mirror symmetry for quasimaps to $X$, including the
Donaldson--Thomas crepant resolution conjecture.
