Are two states equivalent in a DFA if on the same input the states transition to each other?
"We say that states $p$ and $q$ are equivalent if:
  
  
  For all input strings $w$, $\hat{\delta}(p,w)$ is an accepting state if and only if $\hat{\delta}(q,w)$ is an accepting state."
  
  
  (John E. Hopcroft, Rajeev Motwani, and Jeffrey D. Ullman. 2001. Introduction to automata theory, languages, and computation, 2nd edition.)


So if the automaton doesn't accept any strings, there cannot be a string that distinguishes the two states, and therefore there cannot be an equivalence between two states.