  In this work we propose a way to unveil the type of environmental noise in
strongly driven superconducting flux qubits through the analysis of the
Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level
and the multilevel dynamics of the flux qubit driven by a dc+ac magnetic field.
We found that the LZS interference patterns exhibit well defined multiphoton
resonances whose shape strongly depend on the time scale and the type of
coupling to a quantum bath. For the case of transverse system-bath coupling,
the n-photon resonances are narrow and nearly symmetric with respect to the dc
magnetic field for almost all time scales, whilst in the case of longitudinal
coupling they exhibit a change from a wide symmetric to an antisymmetric shape
for times of the order of the relaxation time. We find this dynamic behavior
relevant for the interpretation of several LZS interferometry experiments in
which the stationary regime is not completely reached.
