 In order to elucidate the relationship between our distance between two dynamic metric spaces and the bottleneck distance between their Rips zigzag barcodes, we exploit recent advances in the stability of zigzag persistence ( due to Botnan and Lesnick ).
<clarity>  In order to elucidate the relationship between our distance between two dynamic metric spaces and the bottleneck distance between their Rips zigzag barcodes, we exploit recent advances in the stability of zigzag persistence ( due to Botnan and Lesnick ).
 In order to elucidate the relationship between our distance between two DGs and the bottleneck distance between their Rips zigzag barcodes, we exploit recent advances in the stability of zigzag persistence ( due to Botnan and Lesnick ).