Italy was the first European country to be hit by COVID-19 in the early 2020, since then losing over 100,000 people to the disease. By the end of the vaccination campaign of 2021, 81% of the public received at least one dose. These dramatic developments were accompanied by a rigorous discussion around vaccination, both about its urgency and its possible negative effects. Twitter is one of the most popular social media platforms in the country, but pre-pandemic vaccination debate has been shown to be polarized and siloed into echo chambers. It is thus imperative to understand the nature of this discourse, with a specific focus on the vaccination hesitant individuals, whose healthcare decisions may affect their communities and the country at large. In this study we ask, how has the Italian discussion around vaccination changed during the COVID-19 pandemic, and have the unprecedented events of 2020-2021 been able to break the echo chamber around this topic? We use a Twitter dataset spanning September 2019 - November 2021 to examine the state of polarization around vaccination. We propose a hierarchical clustering approach to find the largest communities in the endorsement networks of different time periods, and manually illustrate that it produces communities of users sharing a stance. Examining the structure of these networks, as well as textual content of their interactions, we find the stark division between supporters and hesitant individuals to continue throughout the vaccination campaign. However, we find an increasing commonality in the topical focus of the vaccine supporters and vaccine hesitant, pointing to a possible common set of facts the two sides may agree on. Still, we discover a series of concerns voiced by the hesitant community, ranging from unfounded conspiracies (microchips in vaccines) to public health policy discussion (vaccine passport limitations). We recommend an ongoing surveillance of this debate, especially to uncover concerns around vaccination before the public health decisions and official messaging are made public.