  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 Jackson's
$q$-analogue of the Pfaff-Saalsch\"utz summation formula from the theory of
basic hypergeometric series.
