DEPARTING BUR; A320 INITIATES TCASII MANEUVER TO AVOID 2 TRANSITING VFR ACFT APPROX 1 MI AT DEP END RWY 15.

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THIRD ACFT INVOLVED. WE WERE ON TKOF ROLL; RWY 15; BUR AND I HEARD US CALLED AS TFC ON THE ROLL TO AN ACFT TRANSITING(?) BUR CTL ZONE. JUST AFTER LIFTOFF; AND IN TURN PER PUBLISHED DEP; BUR TWR POINTED OUT TFC TO US L TO R AT (?) ALT. TFC WAS SPOTTED SLIGHTLY ABOVE AND TO THE R AND CLOSE; BUT THE TURN AND CLB MOMENTUM WAS TAKING US INTO TFC. TCASII ACTIVATED WITH RA TO DSND ALMOST IMMEDIATELY WITH TWR'S TFC CALL. AN EVASIVE L TURN WAS STARTED ALONG WITH COMPLIANCE WITH RA TO DSND. BEFORE THE TRANSITION WAS COMPLETED; WE CLBED THROUGH THE VISUAL TFC'S ALT; BUT TCASII RA CONTINUED TO CALL FOR DSCNT; AND FURTHER INCREASE THE DSCNT. THIS CAUSED SOME CONFUSION SINCE WE WERE NOW ABOVE THE TFC; OR SO WE THOUGHT! THE FO CONTINUED RA COMPLIANCE AND THEN SAW THE SECOND TARGET ON THE TCASII DISPLAY. THIS DISPLAY WAS OVERLAPPING THE ORIGINAL TARGET DISPLAY; AND IN THE INTENSE MOMENT IN OUR FLT DECK; THE SEPARATION ALT OF THIS TARGET COULD NOT BE DETERMINED. THE SECOND TARGET WAS NOT POINTED OUT TO US. BOTH TARGETS WERE WITHIN 1/4 MI AND RIGHT AT THE DEP END OF RWY 15 AT BUR. IT SEEMS BUR TWR; OR VNY TWR; OR SOMEONE SHOULD HAVE BEEN AWARE OF THESE TARGETS/TFC AND LET THEM BE FARTHER DOWN THE ROAD BEFORE WE WERE CLRED FOR TKOF. A DEP WINDOW FOR PHX FLOW CTL FOR US MAY HAVE BEEN A FACTOR.