Are Mary, Marry, and Merry homonyms?

[ilikeverin]

Yes (Midwesterner).  They are all /ɛ/.

Good luck to the people who answered anything other than Option 1 how the three vowels differ from each other.

FWIW, let me try:

"merry" like in "bed"
"Mary" like in "May"
"marry" like in "mad"

Now let's try explaining to the Southerners how "pen" and "pin" sound different, or to the Westerners how "cot" and "caught" sound different

[ilikeverin]

Yes (Midwesterner).  They are all /ɛ/.

Good luck to the people who answered anything other than Option 1 how the three vowels differ from each other.

FWIW, let me try:

"merry" like in "bed"
"Mary" like in "May"
"marry" like in "mad"

Now let's try explaining to the Southerners how "pen" and "pin" sound different, or to the Westerners how "cot" and "caught" sound different

In my native part of the Midwest (Peoria), the last two are absolutely pronounced the same, haha.  Not the pen/pin thing, though.

Yes, "Westerners" is a pretty loose grouping.  The cot-caught merger is starting to cross the Mississippi, although I'd've thought you wouldn't've had it in Peoria.  Also yinzers.  Yinzers should not understand the difference, either.

Yes (Midwesterner).  They are all /ɛ/.

Good luck to the people who answered anything other than Option 1 how the three vowels differ from each other.

FWIW, let me try:

"merry" like in "bed"
"Mary" like in "May"
"marry" like in "mad"

Now let's try explaining to the Southerners how "pen" and "pin" sound different, or to the Westerners how "cot" and "caught" sound different

Bed, May and May (e, ay and a) sounds all sound different.

Yes, they are different (for every English speaker to my knowledge - although exactly what they are realized as will differ from dialect to dialect).  But to people who don't merge, the ones that are unmerged within the context of Mary-marry-merry will sound something the vowels of May-mad-bed (respectively).  Meanwhile, people who do merge will sound like they're saying "merry" for all three of them (using the vowel of "bed").

[ilikeverin]

You pronounce, Barry, Carry, Larry, Marry, Harry the same way?  So, you call someone named Harry, "Hairy?"

Yes, that is precisely what everyone who checked the first option in the poll is saying.

Yes, they are different (for every English speaker to my knowledge - although exactly what they are realized as will differ from dialect to dialect).  But to people who don't merge, the ones that are unmerged within the context of Mary-marry-merry will sound something the vowels of May-bed-mad (respectively).  Meanwhile, people who do merge will sound like they're saying "merry" for all three of them (using the vowel of "bed").

Not quite: the vowel in "Mary" is not that like the one in "May".  For British r-droppers, "mare" and "may" are different words with different vowels, neither has an /r/, and "Mary" is like the first.

Ah!  I didn't see the "historical" before the "/eɪ/" in the Wikipedia article.  Thanks for the correction.

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That's accurate.

[ilikeverin]

You pronounce, Barry, Carry, Larry, Marry, Harry the same way?  So, you call someone named Harry, "Hairy?"

Yes.

Wrong!

Exactly, I agree with Bedstudy.

How can I be wrong about the way I pronounce things?

Fight the good fight, Goldwater!  Down with prescriptivism!