We propose an equality between five-dimensional (5d) Nekrasov partition functions that are associated with local del Pezzo surfaces, namely the generating functions of the refined Gopakumar-Vafa invariants. It is known that M-theory compactified on a local del Pezzo Calabi-Yau 3-fold leads to a 5d superconformal field theory (SCFT), and their BPS partition functions are these Nekrasov partition functions. One can expect that the "Picard-Lefschetz transformation" of the 3-folds implies the duality between the compactified M-theories and the resulting 5d SCFTs. This stringy argument yields conjectural relations between the corresponding Nekrasov partition functions.