fundamental group of $\Lambda(n)$ is infinitely cyclic, which was known already from Arnold’s classical paper [@Maslov]. Two of our axioms are trivially satisfied for the spectral flow of , and the remaining one only requires the computation of the spectra of two simple examples of differential operators as in . The general case when is not assumed, can easily be obtained from the previous case by a simple conjugation by a path of invertible operators. After a brief recapitulation of the Maslov index in Section \[section-Maslov\], and the gap-metric and spectral flow in Section \[section-spectralflow\], we explain all this in detail in Section \[section-proof\] where we prove Theorem \[main\]. Throughout the paper, we aim our presentation to be rather self-contained, and we will just use some well-known facts from Kato [@Kato].\
Finally, we review a recent spectral flow formula for linear Hamiltonian systems by Hu and Portaluri from [@Hu], which they call *a new index theory on bounded domains*. Firstly, we note that the considered families of Hamiltonian systems are continuous with respect to the gap-metric, which follows easily from our approach to Cappell, Lee and Miller’s Theorem. Secondly, we obtain a spectral flow formula in this setting by a 