Conjecture on deformation equivalence of symplectic resolutions

Let $X\to Y$ and $X^+\to Y$ be proper morphisms. They are deformation equivalent if there are deformations $\mathcal X\to\mathcal Y$ and $\mathcal X^+\to\mathcal Y$ over a pointed smooth connected curve $0\in S$, specializing to the given morphisms, such that for a general point $s\in S$ the morphisms

$$\mathcal X_s\to\mathcal Y_s\leftarrow\mathcal X^+_s$$

are isomorphisms. Deformation-equivalence conjecture. Any two symplectic resolutions of a symplectic variety are deformation equivalent. The conjecture is proved for nilpotent orbit closures of classical type, and the paper proves it for projective symplectic resolutions of ${\mathbb C}^4/G$ with finite $G<\operatorname{Sp}(4)$; it remains open in general.