It seems to be a well understood and old topic, but even after a few days of searching, I am having trouble finding a good/more pedagogical introduction to Mapping Class Group of Seifert-Fibered spaces, preferably with examples. I am mostly interested in the typical case $M(+g (g<3),0;\beta_1/\alpha_1,\ldots,\beta_n/\alpha_n)$. Again, my understanding is that MCG is mostly determined by the MCG of base space, but I need to understand it through some explicit examples. Also, is $MCG(M)$ isomorphic to $Out(\pi_1(M))$? And exactly what twistings generates the $MCG(M)$?