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 $\mathcal{O}_{\mathbb{P}^1}(-1)^{\oplus2}$ and the flop is given by contracting the $\mathbb{P}^1$ and "inserting $\mathbb{P}^1$ in other direction".