I don't understand your question. The three completely different words "there," "their," and "they're" are pronounced IDENTICALLY. "There" is always pronounced the same way. In these two sentences, "there" is pronounced the same way. "There is a skyscraper in New York named the 'Empire State Building.'" "There are many skyscrapers in New York." Very very very rarely you may see the contraction "there're" (for "there are.") It is colloquial, it is not in dictionaries. It is used in quoted dialog to show the exact way someone is speaking. Do not try to use yourself. It is pronounced "therur" but with an indefinite "schwa" sound where I've written "u." It is simply what happens naturally when someone say "there are" quickly and with sloppy diction. "There's a skyscraper in New York named the 'Empire State Building.'" <--good English, "there's" is a valid word. "There're a helluva lotta big ol' skyscrapers in N'york." <---NONSTANDARD English.

Because it's easier and more natural to say that way. Even in accents which don't pronounce the 'r' in 'there' pronounce it lightly it phrases such is 'There is'. This is what is known as a 'liaison' - a normally silent consonant which is pronounced when the next word begins with a vowel.

'There'.... I don't pronounce the R much at all. But in 'There is' I sound like I'm saying Theh-Riz.