||In this talk, we consider surfaces embedded in 4-manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary 4-manifold. This extends work of Swenton and Kearton-Kurlin in S^4. As an application, we show that bridge trisections of isotopic surfaces in a trisected 4-manifold are related by a sequence of perturbations and deperturbations, affirmatively proving a conjecture of Meier and Zupan. We also exhibit several isotopies of unit surfaces in CP^2. (i.e. spheres in the generating homology class), proving that many explicit unit surfaces are isotopic to the standard CP^1. This strengthens some previously known results about the Gluck twist in S^4, related to Kirby problem 4.23.