Is there an analogue to the Open University in Italy? By that, I mean a respected public distance-learning university with few/no access barriers. Another institution of this type would be the "FernUniversität in Hagen", in Germany.
There are several distance-based universities in Italy, but not a public or free (as in beer) one, as far as I know; you find a list on https://it.wikipedia.org/wiki/Universit%C3%A0_telematica for instance.
Note that universities (online or not) are not usually free in Italy, though you can apply for tax reductions, full waivers or scholarships based on merit or low income; most prominently, all public universities are free if your family has an income less than 20k€/year.
Some public universities offer MOOCs; for instance the Federico II university of Naples, https://www.federica.eu/en/all-moocs/ or the Politecnico of Milan https://www.pok.polimi.it/ . Even more universities put some recorded lectures online freely accessible to everyone; for instance the one I work for, the university of Pisa, https://mediateca.unipi.it/ .