Although spelt differently, are “Marry”, “Merry” and “Mary” pronounced differently?

British English

In British English (Received Pronunciation), the differences are as follows:

Marry [ˈmær.i] rhymes with “carry”

Merry [ˈmer.i] rhymes with ‘cherry”

Mary [ˈmeə.ri] rhymes with “fairy”

American English

A survey conducted in the US asked: “How do you pronounce marry/merry/Mary?”

1. All 3 are the same (56.88%)
2. All 3 are different (17.34%)
3. Mary and merry are the same; marry is different (8.97%)
4. Merry and marry are the same; Mary is different (0.96%)
5. Mary and marry are the same; merry is different (15.84%)

A very high percentage say that they are all the same, but why?

American vowels becoming more neutral

The main example of vowels becoming more neutral in American is in words with some vowel in front of an [r] that is also followed by another syllable, such as marry or hurry.

[æ] in marry ® [ɛ] in merry ® [ə]
[ei] in Mary ® [ɛ] in merry ® [ə]

Examples give [ei] and [ɛ] merging so that Mary and merry are pronounced identically, and [æ] and [ɛ] merging so that marry and merry sound identical. In cases where these both occur, marry merry Mary sounds like merry merry merry.