  We show that all the standard distances from metric geometry and functional
analysis, such as Gromov-Hausdorff distance, Banach-Mazur distance, Kadets
distance, Lipschitz distance, Net distance, and Hausdorff-Lipschitz distance
have all the same complexity and are reducible to each other in a precisely
defined way.
  This is done in terms of descriptive set theory and is a part of a larger
research program initiated by the authors in \emph{Complexity of distances:
Theory of generalized analytic equivalence relations}. The paper is however
targeted also to specialists in metric geometry and geometry of Banach spaces.
