Abstract: The celebrated theorem of Levinson relates the number of bound states of the Schrödinger operator $-\Delta+V$ to the scattering matrix $S(\lambda)$ of the pair $(-\Delta, -\Delta+V)$ with a correction term accounting for the existence of zero-energy resonances. By considering $S(\cdot)$ as a path of unitaries, we show that the Levinson theorem can be stated as an analytic spectral flow formula for the path of scattering matrices $S(\cdot)$. This perspective provides a unified and analytic framework that works in all dimensions and remains valid both in the presence and absence of resonances.