We propose a duality between various Type IIB 5-brane web configurations, and this conjecture implies an equality between the corresponding 5d Nekrasov partition functions (i.e. refined topological string partition functions) that are associated with local del Pezzo surfaces. It is known that M-theory compactified on a local Calabi-Yau 3-fold leads to a 5d superconformal field theory (SCFT), and this system is dual to a Type IIB 5-brane web system. One can expect that the “Picard-Lefschetz transformation” of these 3-folds implies the duality between these brane setups and the resulting 5d SCFTs. We then find that many different Type IIB 5-brane webs describe the same 5d SCFT that was found by N.Seiberg. We check this duality by comparing the Nekrasov partition functions of these 5-brane web configurations.