  We give a classification of {\texttt{e.a.b.}} semistar (and star) operations
by defining four different (successively smaller) distinguished classes. Then,
using a standard notion of equivalence of semistar (and star) operations to
partition the collection of all {\texttt{e.a.b.}} semistar (or star)
operations, we show that there is exactly one operation of finite type in each
equivalence class and that this operation has a range of nice properties. We
give examples to demonstrate that the four classes of {\texttt{e.a.b.}}
semistar (or star) operations we defined can all be distinct. In particular, we
solve the open problem of showing that {\texttt{a.b.}} is really a stronger
condition than {\texttt{e.a.b.}}
