The third chord in the first measure moves to another position. To play this chord, place the ring finger on the "A" note on the D string and place your middle finger on the "D" note of the A string. The last chord in the first measure slides up to the first chord in the second measure. The interval from "G#" to "D" as mentioned above is a very strong-tensioned E7 chord as it lacks the root note "E".
The first note of the third measure is a unison note played as an open 1st string and the E note stopped by the pinky on the A string. Leave the A string "E" stopped for the next two chords and then play a "D" along with the open "E". These notes resolve to the A chord, in this example a "C#" on the A string and an open "E" on the 1st string. Note, again, here's a double stop lacking the actual root note.
Bobby Hicks and others use these double stops often in their playing. A similar ascension may be heard by listening to Bobby play Maiden's Prayer. Listen closely and you'll hear these and similar intervals.