  We show how wall-crossing formulas in coupled 2d-4d systems, introduced by
Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the
deformation theory of holomorphic pairs, given by a complex manifold together
with a holomorphic vector bundle. The main part of the paper studies the
relation between scattering diagrams and deformations of holomorphic pairs,
building on recent work by Chan, Conan Leung and Ma.
