  We discuss level crossing of the free-energy of TAP solutions under
variations of external parameters such as magnetic field or temperature in
mean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking
(1RSB). We study the problem through a generalized complexity that describes
the density of TAP solutions at a given value of the free-energy and a given
value of the extensive quantity conjugate to the external parameter. We show
that variations of the external parameter by any finite amount can induce level
crossing between groups of TAP states whose free-energies are extensively
different. In models with 1RSB, this means strong chaos with respect to the
perturbation. The linear-response induced by extensive level crossing is
self-averaging and its value matches precisely with the disorder-average of the
non self-averaging anomaly computed from the 2nd moment of thermal fluctuations
between low-lying, almost degenerate TAP states. We present an analytical
recipe to compute the generalized complexity and test the scenario on the
spherical multi-$p$ spin models under variation of temperature.
