I am going to explain how the three words appearing in the title are related. To be more spercific, we consider a type of Lagrangian branes in C^3. Their Ekholm-Shende wavefunctions live in the HOMFLY skein module, encoding open Gromov-Witten invariants in all genus and with arbitrary numbers of boundary components. We develop a skein theoretical cluster theory, prove that these wavefunctions are related to each other under ``cluster mutation'', and hence compute them. This is joint work with Prof. Eric Zaslow and Prof. Gus Schrader.