SYZ geometry for Calabi-Yau 3-folds: Taub-NUT and Ooguri-Vafa type metrics

We construct a family of Calabi-Yau metrics on ${\text{C}}^3$ with properties analogous to the Taub-NUT metric on ${\text{C}}^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.