Watch the G7 Blues Up The Neck: Chords & Licks online guitar lesson by Rob Garland from Melodic Soloing: Blues Chord Tones
So how did I connect the 3rd's & b7th's? I'm seeing a combination of the chord voicings and arpeggios. Play through the arpeggios and look at how my licks use the chord tones with bends and additional tones to spell out the harmony of the chords.
Once again, I'm repeating the main theme and leaving space, connecting chord tones with bends. I also use the minor pentatonic scale on the IV chord to alter the mood after the more melodic chord tones on the I chord. I like the b5 as a tension note. Experiment!