  One of the main applications of resurgence in physics is the decoding of
nonperturbative effects through large order relations. These relations connect
perturbative asymptotic expansions of observables to expansions around other
saddle points. Together, this data is unified in transseries that describe the
nonperturbative structure. It is known that large order relations themselves
also take the form of transseries. We study these large order transseries,
uncover an interesting underlying geometry that we call the `Borel cylinder',
and show that large order transseries in turn are resurgent -- that is: their
nonperturbative sectors `know about each other' through Borel residues that are
essentially equal to those of the original transseries. We show that with an
appropriate resummation prescription, large order relations are often exact:
they can be used to exactly compute perturbative coefficients -- not just their
large order growth. Finally, we argue that Stokes phenomenon plays an important
role for large order relations, for example if we want to extend the discrete
index of the perturbative coefficients to arbitrary complex values.
