The importance of implementing new methodologies to study the ever-increasing amount of Covid-19 data is apparent. The aftermath analysis of these data could inform us on how specific political decisions influenced the dynamics of the pandemic outbreak. In this paper we use the Italian outbreak as a case study, to study six different Covid indicators collected in twenty Italian regions. We define a new object, the Covidome, to investigate the network of functional Covid interactions between regions. We analyzed the Italian Covidome over the course of 2020, and found that Covid connectivity between regions follows a sharp North-South community gradient. Furthermore, we explored the Covidome dynamics and individuated differences in regional Covid connectivity between the first and second waves of the pandemic. These differences can be associated to the two different lockdown strategies adopted for the first and the second wave from the Italian government. Finally, we explored to what extent Covid connectivity was associated with the Italian geographical network, and found that Central regions were more tied to the structural constraints than Northern or Southern regions in the spread of the virus. We hope that this approach will be useful in gaining new insights on how political choices shaped Covid dynamics across nations.