$(1)$ Write step by step mechanism of anionic polymerization of the product obtained from problem $91(p-$methoxystyrene$)$; $(2)$ explain why you call this polymerization is living polymerization; and $(3)$ explain which technique is better for the polymerization of $p-$methoxystyrene, anionic or cationic?

Structural formula, not formula, please!!!!