The chord progression for the introduction is: Am - C+ - C - D7 - F - Fm - C
However, you can see it as Am - C - F - C (or vi - I - IV - I), and the chords in the middle are only chromatic passing notes, i.e.
• In the sequence Am - C you have (A,C,E) that goes to (C,E,G).
E and C are common to both chords and A and G are one tone apart. Add a chromatic ornament in between A and G to obtain the note sequence A - Ab - G, and it may look like you passed through C+, but it is in reality just a passing note.
• Between C (C,E,G) and F(F,A,C), E goes to F through F#, and G goes to A through Ab, looking like you passed through D7.
• Finally to go form F(F,A,C) to C(C,E,G), A goes to G through Ab and F remains to go directly to E, looking like you passed through Fm.
This way you can see that you are in the key of C all the time, and all strange notes are in fact chromatic passing notes. Passing notes always create tension since they are not part of the chord and therefore create a dissonance (and chromatic passing notes create even more tension since they are not part of the key), which is released once they resolve to a note that is part of the chord, so concerning the specific part you ask about (IV-iv-I) you have a simple plagal cadence with a chromatic passing note.
Of course this is just an interpretation, but at least the way I learned analysis, the goal is to explain the harmony with as little chords and modulations as possible, as long as the remaining notes fall into the category of an embellishment note.