Rush vs The Beatles

The Beatles I have to admit the Beatles for  a mainstream band they were really progressive and even jazz music were not doing some of the things they were doing like backward guitar, drum looping to name a few. Some of their rhythms on "Happiness Is A Warm Gun" for example include a Balkan rhythm and a polyrhythm in different sections. Were they influenced by jazz?

"A Day in the Life", "I am the Walrus", "Within You, Without You", Strawberry Fields"... not really blues tunes, They were able to draw from diverse sources, like Indian classical music  "Within You" uses a raga-like form that contains both major and minor thirds in different octaves, kind of a combination of mixolydian and Dorian modalities. Lennon used forms similar to Tibetan chants. McCartney and Lennon were both versed in the same types of cadential cycles that had evolved from Dixieland and Tin Pan Alley, the pop music of the previous era (and also a primary underpinning for jazz).

"Tomorrow Never Knows" is a very early Art-Rock song that was recorded even before the Velvet Underground. The song is influenced by Avant music and its weird sounds are produced by tape loops/samples with looped effects. The song uses an upfront drum 'n' bass sound with the looped effects not unlike many forms of Modern Music.

I considered "Strawberry Fields Forever" true progressive rock songs. With its use of mellotron, Indian scales and two separate versions of one song into one.  Strawberry Fields Forever" uses diminished chords that are common with jazz music. Then are changes time signatures often 4/4, 6/8, 3/4, 2/4. Hardly simple stuff. It helped invent Progressive Rock.

"Blue Jay Way" song based on some ancient Indian raga that uses the diminished 7th scale. 

I think the Beatles were one of the biggest influences in early progressive rock.