Before revision:  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 ).
After revision:  In order to elucidate the relationship between our distance between two dynamic metric spaces and the bottleneck distance between their associated barcodes, we exploit recent advances in the stability of zigzag persistence ( due to Botnan and Lesnick ).