ACR TAKES EVASIVE ACTION; TURN AND CLB WITH VISUAL SIGHTING ON SMA. TCASII TA; NO RA. ATC QUESTIONS ALT.

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ON INITIAL CLB FROM BURBANK ARPT. CLRED TO 13000 FT INITIALLY IN A TCASII EQUIPPED ACFT WITH MANY VFR AND IFR ACFT IN THE VICINITY. INITIAL HDG AFTER TKOF WAS 210 DEG. DEP ASKED FOR US TO EXPEDITE OUR CLB FOR 12 O'CLOCK TFC AT 4500 FT AND TO MAINTAIN 6000 FT. WE WERE GIVEN A TURN TO 280 DEG AND ADVISED OF TFC AT 2 O'CLOCK WHICH WAS WBOUND AT 6500 FT. NEXT WE WERE GIVEN A TURN TO 340 DEG AS WE LEFT 5000 FT FOR 6000 FT. THESE EVENTS TOOK PLACE IN A VERY SHORT PERIOD OF TIME AND COCKPIT WORKLOAD WAS VERY HIGH. I WAS FLYING THE ACFT AT THE TIME AND SAW THE SMA AT 2 O'CLOCK TFC WHO APPEARED TO BE AT OUR ALT AND ALSO APPEARED TO BE DIRECTLY IN OUR PATH LESS THAN A MI AWAY. I INITIATED A TURN BACK TO THE L IMMEDIATELY TO AVOID THE SMA; BECAUSE IT APPEARED THAT IF WE CONTINUED IN THE CLRED DIRECTION WE WOULD HAVE COME DANGEROUSLY CLOSE TO THE ACFT. THROUGHOUT THIS TIME; TCASII WAS GIVING TA'S EITHER THE SMA WAS NOT ENCODING OR OUR TCASII WAS NOT PICKING THE ACFT UP BECAUSE OUR DISTANCE AND CLOSURE RATE SHOULD HAVE GENERATED AN RA. DURING OUR RAPID EVASIVE MANEUVER; OUR ALT INCREASED TO ABOUT 6600 FT WHICH SEEMED TO BE ABOVE THE SMA ALT. ATC QUESTIONED OUR FAILURE TO LEVEL AT 6000 FT; WE REPLIED THAT WE HAD MANEUVERED RAPIDLY AND VISUALLY WITH REF TO THE SMA AS OUR ORIGINAL VECTOR OF 340 DEG HAD US CLOSING RAPIDLY ON THE SMA. THE L CLBING TURN SEEMED TO BE THE BEST DIRECTION AWAY FROM THE SMA DUE TO OUR SPD 230 KTS AND ACCELERATING WITH THE 340 DEG HDG PUT US WITH 15 SECONDS OF A POSSIBLE COLLISION. ALTHOUGH WE DID NOT BECOME AN EMER FOR OUR MANEUVER DUE TO THE LACK OF TIME AND RADIO CONGESTION THIS WAS ESSENTIALLY AN EMER MANEUVER IN OUR VIEW. CONTRIBUTING FACTORS: RAPID CLB RATE; NUMEROUS TA'S FROM TCASII AND ATC; CITY SMOG; RADIO CONGESTION.