Alternating automata In the paper Fast LTL to Buchi Automata Translation (2001, Gastin and Oddoux)  the authors, while defining co-Buchi alternating automata define  $\Sigma’= 2^\Sigma$ where $\Sigma$ is the alphabet.
They say that because of this the transitions that differ only by action can be gathered. 

What does this statement exactly mean? Any pointers will be helpful.

thanks
Expanding on Markus' answer a bit, note that the alphabet $\Sigma$ is in turn the powerset $2^{Prop}$ of the set $Prop=\{p_1,\dots,p_k\}$ of atomic propositions, i.e. it represents the set of valuations $a:Prop\to\{T,F\}$ of the $p_i$.

In the LTL formula, most boolean subformulas involve only a few of the propositions. In the translation, any such subformula corresponds to the set of all valuations $a\in\Sigma$ satisfying it, which is typically large. Using $\Sigma'$, you still only have one transition.

For example, Figure 1 in the paper shows an automaton with transitions labelled simply by $p$ or $q\wedge\neg r$ (where $p,q,r$ are the propositions from the formula). Using $\Sigma$, for the first you would instead have four transitions labelled $\{p\},\{p,q\},\{p,r\},$ and $\{p,q,r\}$.