In the gluing region $x_{1}\sim\tilde{C}x_{2}$, namely $x_{1},x_{2}$ and $\tilde{x}_{1}$ are comparably large, the deviation between $\phi_{D_{1}}^{(2)}$ and $u$ comes from the $O(e^{-cx_{2}^{1/2}})$ small deviation between the Tian-Yau potential and the Calabi ansatz, and the correction term $\tilde{x}_{1}^{\frac{n+2}{n}-\frac{2n}{n-1}}U$. Ignoring the exponentially small effects, the only important term is $\tilde{x}_{1}^{\frac{n+2}{n}-\frac{2n}{n-1}}x_{2}^{\frac{1}{n-1}}$. We compute from Lemma 4.7

$$\left\lVert dd^{c}(\eta\tilde{x}_{1}^{\frac{n+2}{n}-\frac{2n}{n-1}}x_{2}^{\frac{1}{n-1}})\right\rVert_{k,\alpha,loc}=O(x_{1}^{\frac{n+2}{n}-\frac{2n}{n-1}+\frac{1}{n-1}-2+\frac{n-2}{n}})=O(x_{1}^{-\frac{2n-1}{n-1}}).$$

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