General American pronunciation is fully rhotic, the /r/ is usually pronounced by most Americans (including Canadians). Exception: some traditional east-coast accents, as well as some African-American accents, are “non-rhotic” — they drop the final /r/ in much the same way as RP speakers do. The exact realization of the vowel, as well as the use of “linking-R”, will depend on the region and speaker. /ðeərɪz/ is the pronunciation of “there is” (although the /ɪ/ will usually be reduced to a schwa unless “is” is stressed for emphasis). The contraction “there’s” is pronounced as a single syllable, /ðeərz/. The same goes for “more’s”.