As Bridgeland observed [13, Thm 1.2], the central charge map gives a local homeomorphism between the space of Bridgeland stability conditions, and the hom space from the numerical Grothendieck group to $\mathbb{C}$. The Thomas-Yau-Joyce philosophy then suggests that for fixed $\omega$ and small deformations of $\Omega$, the stability condition only depends on the cohomology class $[\Omega]$.

A possible geometric interpretation consistent with the wall crossing picture, is that in a generic 1-parameter family of deformations of the almost Calabi-Yau structure fixing $\omega$ and $[\Omega]$, the special Lagrangian may undergo surgeries, such that the topology and the Hamiltonian isotopy class may change, but when equipped with the brane structures, the $D^{b}Fuk(X)$ class (or possibly some weaker equivalence class) remains constant. As in the LMCF approach, the role of the unobstructed brane structure is morally to prevent holomorphic discs from having very small area. However, the troubles caused by shrinking discs may be less severe in the continuity method than in the LMCF method, since the continuity method only deals with special Lagrangians, and cannot lose grading in a process like Example 4.3. Instead, a significant amount of difficulty in the continuity method is absorbed into the problem of finding the initial special Lagrangians.