The t-invariant of analytic set germs of dimension 2

Let image be an analytic set germ of dimension 2. We study the invariant t(X0) defined as the least integer t such that any open semianalytic set germ of X0 can be written as a union of t basic open set germs. It is known that 2≤t(X0)≤3. In this note we provide a geometric criterion to determine the exact value of t(X0).