What is this merger called? I know there's the nearer-mirror merger, where both words are pronounced with the exact same long i, but which merger is responsible for the pronunciation of the short i in the "be" part of the word 'believe'? The singer is Dan Tyminski, who was born in Rutland, Vermont.
At first, I thought it was the southern drawl:
Stage 3 (/i/ → [ɪi] and /ɪ/ → [iə]): By the same pushing and pulling domino effects described above, /ɪ/ (as in hit or lick) and /i/ (as in beam or meet) follow suit by both possibly becoming diphthongs whose nuclei switch positions. /ɪ/ may be pushed into a diphthong with a raised beginning, [iə], while /i/ may be pulled into a diphthong with a lowered beginning, [ɪi]. An example is that, to other English speakers, the Southern pronunciation of fin sounds something like fee-in, while meal sounds something like mih-eel. Like the other stages of the Southern shift, Stage 3 is most common in heavily stressed syllables and particularly among Inland Southern speakers. Wikipedia
but there's obviously no drawling in there. Then, I thought it was the fill-feel merger as there's an L sound in "believe":
Lax and tense vowels often neutralize before /l/, making pairs like feel/fill and fail/fell homophones for speakers in some areas of the South. Some speakers may distinguish between the two sets of words by reversing the normal vowel sound, e.g., feel in Southern may sound like fill, and vice versa. Wikipedia
The fill–feel merger is a conditioned merger of the vowels /ɪ/ and /iː/ before /l/ that occurs in some dialects of American English. The heaviest concentration of the merger is found in, but not necessarily confined to Southern American English: in North Carolina, eastern Tennessee, northern Alabama, Mississippi, Louisiana (but not New Orleans), and west-central Texas (Labov, Ash, and Boberg 2006: 69-73). This merger, like a lot of other features of Southern American English, can also be found in AAVE. Wikipedia
And this seems like a plausible theory, but I don't think I'm right.