We report on the modeling, simulation and experimental demonstration of complete mode crossings of Fano resonances within chip-integrated microresonators. The continuous reshaping of resonant lineshapes is achieved via nonlinear thermo-optical tuning when the cavity-coupled optical pump is partially absorbed by the material. The locally generated heat then produces a thermal field, which influences the spatially overlapping optical modes, allowing thus to alter the relative spectral separation of resonances. Furthermore, we exploit such tunability to probe continuously the coupling between different families of quasi-degenerate modes that exhibit asymmetric Fano-interactions. As a particular case, we demonstrate for the first time a complete disappearance of one of the modal features in the transmission spectrum as predicted by U. Fano [Phys. Rev. 124, 1866 (1961)]. The phenomenon is modeled as a third order non-linearity with a spatial distribution that depends on the stored optical field and the thermal diffusion within the resonator. The performed non-linear numerical simulations are in excellent agreement with the experimental results, which confirm the validity of the developed theory. ; Comment: 9 pages, 8 figures