After some research, I ended up building it on my own. I carefully followed every redirect, and took note of every cookie created, edited or deleted (Opera, with its in-built option which allows to switch off redirects was the key). The result was a flow which then I replicated in a package ad hoc: the SetUpConnection class, whose task was connecting to the host and keeping track of the cookies. SAML class, which replicated the SAML flow, and finally the Main class, from which I can gather useful information.
Hope it helps.