For simple flops X dashrightarrow X', the genus 0 descendant Gromov-Witten theories correspond and this matches the Fourier-Mukai equivalence.
Iritani,An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv
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Descendant and Fourier-Mukai equivalences for simple flops
For simple flops X dashrightarrow X', the genus 0 descendant Gromov-Witten theories correspond and this matches the Fourier-Mukai equivalence.