(cf. [53, section 4.5]) Let $\phi_{0}$ be an Alexandrov solution of the real MA equation (17) on the interior of $\Delta_{J}$. Suppose the Calabi-Yau metrics on $U_{J,t}$ admit local potential functions $\phi_{CY,J,t}$ such that $\omega_{CY,t}=dd^{c}\phi_{CY,J,t}$, and $\left\lVert\phi_{CY,J,t}-\phi_{0}\circ\text{Log}_{\mathcal{X}}\right\rVert_{C^{0}}\to 0$ as $t\to 0$. Then after slightly shrinking $U_{J,t}$, we have the $C^{\infty}$-asymptote $\left\lVert\phi_{CY,J,t}-\phi_{0}\circ\text{Log}_{\mathcal{X}}\right\rVert_{C^{k}_{loc}}\to 0.$