  Magnitude is a numerical invariant of metric spaces and graphs, analogous, in
a precise sense, to Euler characteristic. Magnitude homology is an algebraic
invariant constructed to categorify magnitude. Among the important features of
the magnitude of graphs is its behaviour with respect to an operation known as
the Whitney twist. We give a homological account of magnitude's invariance
under Whitney twists, extending the previously known result to encompass a
substantially wider class of gluings. As well as providing a new tool for the
computation of magnitudes, this is the first new theorem about magnitude to be
proved using magnitude homology.

Combinatorics;Algebraic Topology;Category Theory;Metric Geometry