  The aim of this paper is to show the gauge-invariance on the response of
interferometers to gravitational waves (GWs). In this process, after a review
of results on the Tranverse-Traceless (TT) gauge, where, in general, the
theoretical computations on GWs are performed, which is due for completness, we
analyse the gauge of the local observer, which represents the gauge of a
laboratory environment on Earth. The gauge-invariance between the two gauges is
shown in its full angular and frequency dependences. In previous works in the
literature this gauge-invariance was shown only in the low frequencies
approximation or in the simplest geometry of the interferometer in respect to
the propagating GW (i.e. both of the arms of the interferometer are
perpendicular to the propagating GW). As far as the computation of the response
functions in the gauge of the local observer is concerned, a common
misconception about interferometers is also clarifed.
