In words like winter, center, Atlantic, in which ambisyllabic /t/ follows /n/, a number of rules can apply:
Flapping can apply after (nasalization and) nasal deletion. GA /wɪntər/ becomes [wɪ᷈tər], and, because ambisyllabic /t/ is now between vowels, then becomes [wɪ᷈ɾər].
t/d-deletion may apply to produce [wɪ᷈nər]. In practice, because the nasalization is likely to be maintained during the flap, the members of pairs like winter – winner will tend to be homophonous in unguarded speech.
Notice also in this connection that the following two utterances are distinct because of the /æ/ – /ə/ opposition in can’t – can:
you can’t eat it – [jəkæ᷈ɾiːɾɪt]
you can eat it – [jəkən iːɾɪ]
However, the following two sentences would be (near-)homophonous.