We prove two multivariate $q$-binomial identities conjectured by Bousseau, Brini and van Garrel [Stable maps to Looijenga pairs, arXiv:2011.08830] which give generating series for Gromov-Witten invariants of two specific log Calabi-Yau surfaces. The key identity in all the proofs is Jacksons $q$-analogue of the Pfaff-Saalschutz summation formula from the theory of basic hypergeometric series.
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