I need to build a DFA from $\varepsilon$NFA, so first of all I assume that I need to convert the $\varepsilon$NFA to NFA and then to DFA (because I know the method of converting from NFA to DFA, and we learn how to remove $\varepsilon$'s from $\varepsilon$NFA and make it NFA.
But the I'm still stuck at some cases....
For example:
See this $\varepsilon$NFA:
I want to make it NFA (I don't know if to write the whole algorithm...), and I'm not sure which is right:
Or this (at the comments.... I can't put more then 2 images)
I think that the first is the right one, but I'm not sure...
At the second one - the number of the 0-s must be even to be at $q_1$ but at the original $\varepsilon$NFA it can be any number of 0-s...
One more thing, it's correct that I'm not putting 0,1 insted of the $\varepsilon$? (Because 1 from $q_0$ brings me to $\varnothing$...)