Is it true that any flop on a Calabi-Yau threefold is given by the Atiyah flop? That is, there always exists a rigid rational curve $\mathbb{P}^1$ with normal bundle $\mathcal{O}_{ …

Hi, I'm trying to understand the group of cycles (modulo numerical equivalence) contracted by a flopping contraction $f$. More precisely, I'm in the setup of Definition 2.12 of t …