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We report the results of polarization resolved reflectivity experiments in GaAs air-bridge photonic crystals with L3 cavities. We show that the fundamental L3 cavity mode changes, in a controlled way, from a Lorentzian symmetrical lineshape to an asymmetrical form when the linear polarization of the incident light is rotated in the plane of the crystal. The different lineshapes are well fitted by the Fano asymmetric equation, implying that a Fano resonance is present in the reflectivity. We use the scattering matrix method to model the Fano interference between a localized discrete state (the cavity fundamental mode) and a background of continuum states (the light reflected from the crystal slab in the vicinity of the cavity) with very good agreement with the experimental data. [ABSTRACT FROM AUTHOR]