# State-elimination on FSA, after epsilon-removal construction

I want to define the language of this FSA with a regular expression. I have learned that by state-elimination, I would be able to find a regular expression.

But there are already some epsilon transitions in this FSA.

My question is:

Should I first follow the epsilon-removal construction, and then do state elimination?

Or can I use state-elimination directly on this FSA?

By the way, the regular express I got is $$\left(0+(0+02)(2+42)^*(4+\epsilon)\right)^*(0+02)(42+2)^*\,.$$