Why does switching to half-tone higher feel so smooth here?

The song is Close To You by Carpenters. There's a part where it switches to higher half tone. Say we are already in Em and it's time we went to Fm (Ab major).

For that they employ these chords Cmaj9, Cadd9, C, Cadd9, Bm7 and by this point they have switched to Dbmaj9, Csus4, C, Cm7, Fm7 (...) already in the key of Fm/Ab.

Why does this sound so smooth? What is the link between Bm7 (v of Em) and Db (VI of Fm)?

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