 We define a new filtration called the cover filtration built from a single cover based on a generalized  Jaccard distance.
<meaning-changed>  We define a new filtration called the cover filtration built from a single cover based on a generalized  Jaccard distance.
 We define a new filtration called the cover filtration built from a single cover based on a generalized Steinhaus distance, which is a generalization of Jaccard distance.