Conceptions of Topological Transitivity
  There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various equivalences are proved in different places, but the full story is difficult to find. This note provides a complete description of the relationships among the different properties. 
Ethan Akin and Jeffrey D. Carlson
math.DS