  We present an analytic theory of quantum criticality in the quasi
one-dimensional topological Anderson insulators of class AIII and BDI. We
describe the systems in terms of two parameters $(g,\chi)$ representing
localization and topological properties, respectively. Surfaces of half-integer
valued $\chi$ define phase boundaries between distinct topological sectors.
Upon increasing system size, the two parameters exhibit flow similar to the
celebrated two parameter flow describing the class A quantum Hall insulator.
However, unlike the quantum Hall system, an exact analytical description of the
entire phase diagram can be given. We check the quantitative validity of our
theory by comparison to numerical transfer matrix computations.
