  We show that curve enumeration invariants of complex threefolds with nef
anti-canonical bundle are determined by their values on local curves. This
statement and its proof are inspired by the proof of the Gopakumar--Vafa
integrality conjecture by Ionel and Parker. The conjecture of Maulik, Nekrasov,
Okounkov, and Pandharipande relating Gromov--Witten and
Donaldson--Pandharipande-Thomas invariants is known for local curves by work of
Bryan, Okounkov, and Pandharipande, hence holds for all complex threefolds with
nef anti-canonical bundle (in particular, all Calabi--Yau threefolds).
