How does one read aloud Vinogradov's notation $\ll$ and $\ll_{\epsilon }$?

As a default, I second Gerry Myerson's answer "less-than-less-than", although just reading "sub-epsilon" seems a little odd. In a situation where I'm trying to reinforce the meaning, I might read $A\ll B$ as "$A$ is dominated by $B$", and $A\ll_\varepsilon B$ as "$B$ dominates $A$ depending on $\epsilon$", but this may be defeating the purpose/intent of the question. (Edit: or, better, as noted by Americo Tavares, to say "$A$ is dominated by $B$ depending on $\varepsilon$", to avoid the need to read ahead...)

I read $\ll$ as "less than less than". I don't think I have ever put $\ll_{\epsilon}$ in words, but if I did it would probably come out "less than less than sub epsilon".

"Controlled by a constant multiple of ..., with the constant possibly depending on epsilon", or if you don't want to be quiet as you write it on blackboard, "less less sub epsilon".