Can you skip epsilon transitions in union expression (Thompson's construction algorithm)

Question

In the picture below can I use both NFA interchangeably? If not then why?

Answer 1

Yes, they are equivalent (they recognize the same language). More formally:

First, let's give names to your states:

Now, through powerset construction, let's remove the epsilon transitions:

Finally, we can use any DFA minimization algorithm such as Brzozowski's (reverse the arrows, apply powerset construction again, re-reverse the arrows) to obtain your resulting DFA.