  Two-loop multi-leg form factors in off-shell kinematics require knowledge of
planar and nonplanar double box Feynman diagrams with massless internal
propagators. These are complicated functions of Mandelstam variables and
external particle virtualities. The latter serve as regulators of infrared
divergences, thus making these observables finite in four space-time
dimensions. In this paper, we use the method of canonical differential
equations for calculation of (non)planar double box integrals in the near
mass-shell kinematical regime, i.e., where virtualities of external particles
are much smaller than the Mandelstam variables involved. We deduce a basis of
master integrals with uniform transcendental weight based on the analysis of
leading singularities by means of the Baikov representation as well as an array
of complementary techniques. We dub the former asymptotically canonical since
it is valid in the near mass-shell limit of interest. We iteratively solve
resulting differential equations up to weight four in terms of multiple
polylogarithms.
