Virtual class wall-crossing conjecture for stable quasi-maps

Let $\tau:{\mathcal C}_+\to \mathfrak{Q}_{g,m,d,n}^{\delta_+}$ be the universal curve, with universal family of quasi-maps and wall-crossing morphism $\psi_{\delta_+,\delta_-}:\mathfrak{Q}_{g,m,d,n}^{\delta_+}\to\mathfrak{Q}_{g,m,d,n}^{\delta_-}$ obtained by elementary modification. Virtual class wall-crossing conjecture.

$$(\psi_{\delta_+,\delta_-})_*[\mathfrak{Q}_{g,m,d,n}^{\delta_+}]^{\mathrm{vir}}=[\mathfrak{Q}_{g,m,d,n}^{\delta_-}]^{\mathrm{vir}}.$$

If true, this would imply that the curve-counting invariants obtained from the moduli spaces of $\delta$-stable quasi-maps are independent of the stability parameter $\delta$.