  We describe a correspondence between the virtual number of torsion free
sheaves locally free in codimension 3 on a Calabi-Yau 3-fold and the
Gromov-Witten invariants counting rational curves in a family of orbifold
blowups of the weighted projective plane $\mathbb{P}(-ch_3, ch_0, 1)$ (with a
tangency condition of order $gcd(-ch_3, ch_0)$). This result is a variation of
the GW/quiver representations correspondence found by Gross-Pandharipande, when
one changes the centres and orders of the blowups. We build on a small part of
the theories developed by Joyce-Song and Kontsevich-Soibelman for wall-crossing
formulae and by Gross-Siebert-Pandharipande for factorisations in the tropical
vertex group.
