Surgery diagrams provide an efficient description of smooth 3–manifolds, and Kirby’s theorem shows that any two such diagrams of the same smooth 3–manifold are related by a finite sequence of blowups, blowdowns, and handleslides. In the contact setting, contact 3–manifolds can likewise be encoded by Legendrian surgery diagrams, where the surgery coefficients are restricted to ±1 relative to the Thurston–Bennequin framing. In this talk I will present a complete set of Legendrian Kirby moves relating diagrams of the same contact 3–manifold, yielding a contact analogue of Kirby’s theorem. Our approach refines Avdek’s ribbon moves by using Gervais’ presentation of mapping class groups using only nonseparating curves, together with explicit constructions of Legendrian representatives. This is joint work with Marc Kegel and Eric Stenhende.