The old “glue–and–cut” symmetry of massless propagators, first
established in [1], leads — after reduction to \ice{corresponding} master integrals
is performed — to a host of non-trivial relations between the latter.
The relations constrain the master integrals so tightly that they all can
be analytically expressed in terms of only few, essentially
trivial, watermelon-like integrals. As a consequence
we arrive at explicit analytical results for all master
integrals appearing in the process of reduction of massless
propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas ($\zeta_{2n}$)
in the Adler function and other similar functions essentially reducible
to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.
