I've attempted to search and google related topics and found these two: here and here, although, I'm afraid I don't get their points and I don't know if those would help. I just want to ask and convince myself whether there is or there is not a vowel epsilon /ε/ in English. Is this letter used by some people and there are some don't?'
I see here, that AmE has this letter, for example the noun bed is written as
/ˈbɛd/
according to Learner's Dictionary (app version, the same producer as M-W). However, OALD, CALD, Longman use the letter /e/ like this:
/ˈbed/
Please, look at this diagram I found (screenshoted by someone, I found it on Facebook):
As you can see there that those letter (/e/ and /ε/) are different. I've checked the third link (above). There's a play button to hear the vowel /ε/ and it has exactly the same sound with the vowel /e/ I've watched from BBC English learning (I hope I didn't misheard). Now, I'm confused.

