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I was flipping through Puget Sound's free music theory book, and saw this page https://musictheory.pugetsound.edu/mt21c/i-VII-VI-VII.html

Why did he write the i–VII–VI–VII progression as Am–G–F–G instead of Am-G#-F#-G#. And why did he not write out i-bVII-bVI-bVII ?

He writes out a similar progression but notes that it is 1-b7-b6-5 and I find this confusing.

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First, Roman numeral analysis presumes natural minor, so G and F are correct for the VII and VI chords in A minor.

There are various conventions for writing Roman numerals for music. The one being adhered to here uses VII for the "seven chord" in minor, because the "flat seven" is native to the key (i.e., not an alteration to the underlying scale) and because it's a major chord. For a major key the symbol would be viio.

(See also: Why the flat roman numerals in minor when they aren't needed?)

However, when describing the 1-b7-b6-5 bass line, individual scale degrees are being specified (as opposed to chords), and the mode is not indicated. In this case, major is the reference point, so the flats are included.

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