 We provide stability results for the cover filtration and show how the construction is equivalent to the Cech filtration under certain settings  .
<meaning-changed>  We provide stability results for the cover filtration and show how the construction is equivalent to the Cech filtration under certain settings  .
 We provide stability results for the cover filtration and show how the construction is equivalent to the Cech filtration under certain settings , and the Vietoris-Rips filtration completely determines the cover filtration in all cases .