/ɛ/ and /e/ (or /eI/ or other variations depending on dialect and position), generally contrast. Bet /bɛt/ and bait /bet/ are distinguished. However, before certain consonants such as /r\/, the distinction between tense and lax vowels is neutralized. Therefore any tense or lax vowel before /r\/ is considered to be neither tense nor lax. Thus, /ɛr\/ and /er\/ are both the same in General American. Although this is technically true, I tend to think of vowels before /r\/ as sounding like lax vowels usually.

Some dialects, such as speakers with the Canadian or California vowel shifts will pronounce /E/ as [æ]. This occurs before any consonant, so "bet" "pet" and "clarity" will all have [æ].

Some East Coast US dialects have more distinctions than other North American dialects, and some even distinguish /E/ and /e/ before /r\/, etc. However, these dialects are in usually not regarded as being very close to General American English, and thus I wouldn't recommend learning them. Also some Atlantic Canadian dialects have some other variations, but these are also not General American English.

General American English has lost many distinctions before "r", so Mary merry and marry all have [Er\], as do very and vary. Thus they are all pronounced identically.

Yeah, I knew that's what he meant. He must speak a language that has final consonant devoicing, or no voice-voiceless distinction in word final position, or a language that has no /z/.

I think you would do well to listen to the words below at www.m-w.com to learn the pronunciation of the six R-colored vowels of American English.

deer             moor
care    fur     core
          tar

These are the vowel-plus-R sounds used by most Americans.
There are a few others used in more limited geographical regions, as described by Marvin, but those are not really necessary if you just want to learn a typical sort of American pronunciation.

CJ