But the becomes bə ðə what name is this process?

[semantics12345]

what do we call this process ?

But the ------- bə ðə

But by ------- bə baɪ

[AiWin]

Phonetic transcription?

[semantics12345]

No, I mean when we pronounce these two words together as bə ðə ????

[BobK]

No, I mean when we pronounce these two words together as bə ðə ????

Elision of the /t/ phoneme by assimilation to the following dental fricative.

b

[5jj]

My understanding of elision and assimilation is that they are two different things. Thus, for example, /t/ is frequently elided (or dropped) in next week: /neks wiːk/, and assimilated (or modified) to /p/ in that boy:/ðæpbɔI/

In my own dialect, Southern English RP, I would say that the /t/ in but the assimilates to a glottal stop, /ʔ/