This study proposes a co-bubble network to capture the transmission of co-bubbles across the prices of 37 cryptocurrencies from both static and dynamic perspectives. It considers the periods of the COVID-19 pandemic and the Russo-Ukrainian conflict, and distinguishes clean from dirty cryptocurrencies. The main findings are summarized as follows: Firstly, larger cryptocurrencies, such as Bitcoin, Ethereum, and BNB, have a higher probability of generating co-bubbles in other cryptocurrencies, indicating a strong interdependence among them. Secondly, the co-bubble network experiences notable changes around crisis events, with distinct characteristics observed during the COVID-19 pandemic compared to the Russo-Ukrainian conflict. Thirdly, the transmission of co-bubble influence exhibits time-varying characteristics, and centrality rankings of influential cryptocurrencies vary around the crises. Particularly, after the COVID-19 pandemic, Bitcoin and BNB experience a decline in centrality ranking, while smaller-cap cryptocurrencies show higher centrality rankings, suggesting the transmission of co-bubble effects from large to smaller cryptocurrencies. The centrality rankings of Bitcoin, Ethereum, and BNB show a contrasting pattern, maintaining higher levels in the ongoing post Russo-Ukrainian conflict period. Fourthly, different patterns of co-bubble transmission exist for dirty and clean groups, with dirty cryptocurrencies showing a much higher intensity of co-bubbles during the Russo-Ukrainian conflict. Finally, the portfolio analysis shows that co-bubble network centrality-driven portfolios outperform the baseline portfolio strategy, dirty group portfolio strategy, and clean group portfolio strategy, during the entire sample period and particularly the COVID-19 pandemic. The findings are useful for the decision making of cryptocurrency portfolio managers and policymakers concerned with the behaviour of influential cryptocurrencies and potential risks inferences.