In the region $\{\text{dist}_{g_{a}}(\cdot,\mathfrak{D}_{1})\lesssim A^{1/2}\lesssim|\vec{\mu}|_{a}\}\subset M^{+}_{\nu}$, the Kähler ansatz is approximated by the suitably gauge fixed metric model $g_{\text{Taub}}$, with metric deviation estimate

$$\left\lVert\tilde{g}^{(1)}-g_{\text{Taub}}\right\rVert_{C^{k,\alpha}_{0,0}}\leq CA^{-3/4}\nu,\quad\left\lVert\tilde{\Omega}^{(1)}-\Omega_{\text{Taub}}\right\rVert_{C^{k,\alpha}_{0,0}}\leq CA^{-3/4}\nu.$$

Similarly with the neighbourhood of $\mathfrak{D}_{2}$ and $\mathfrak{D}_{3}$.