Vaccine hesitancy is currently recognized by the WHO as a major threat to global health. Recently, especially during the COVID-19 pandemic, there has been a growing interest in the role of social media in the propagation of false information and fringe narratives regarding vaccination. Using a sample of approximately 60 billion tweets, we conduct a large-scale analysis of the vaccine discourse on Twitter. We use methods from deep learning and transfer learning to estimate the vaccine sentiments expressed in tweets, then categorize individual-level user attitude towards vaccines. Drawing on an interaction graph representing mutual interactions between users, we analyze the interplay between vaccine stances, interaction network, and the information sources shared by users in vaccine-related contexts. We find that strongly anti-vaccine users frequently share content from sources of a commercial nature; typically sources which sell alternative health products for profit. An interesting aspect of this finding is that concerns regarding commercial conflicts of interests are often cited as one of the major factors in vaccine hesitancy. Further, we show that the debate is highly polarized, in the sense that users with similar stances on vaccination interact preferentially with one another. Extending this insight, we provide evidence of an epistemic echo chamber effect, where users are exposed to highly dissimilar sources of vaccine information, depending the vaccination stance of their contacts. Our findings highlight the importance of understanding and addressing vaccine mis- and dis-information in the context in which they are disseminated in social networks.