Kirby calculus changes framed-link diagrams by handle slides and creation or cancellation of standard handle pairs without changing the represented four-manifold up to diffeomorphism.
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Kirby calculus is a mathematical technique used in the field of low-dimensional topology, particularly in the study of 3-manifolds. It is named after Rob Kirby, who introduced this concept in a series of papers in the 1970s. The main focus of Kirby calculus is on the manipulation and understanding of 3-manifolds via the use of specific types of diagrams called Kirby diagrams or handlebody diagrams.