B737 CREW HAVE AN NMAC WITH A SEL CESSNA ABOVE THE BOSTON CLASS B AIRSPACE.

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WHYBE SID OUT OF LOGAN. RECEIVED VECTOR AND CLB '290 DEGS; CLB TO 13000 FT AT 2000 FPM RATE OF CLB. TCASII ALERT OF ACFT LESS THAN 5 NM AT 11 O'CLOCK POS.' BY THE TIME I LOOKED AT THE ALERT SYMBOLOGY; IT HAD TURNED YELLOW AND QUICKLY TURNED RED; WITH AN RA TO DSND. I INITIATED THE DSCNT FROM A 2000 FPM CLB WHILE THE TCASII SYMBOLOGY WENT TO ZERO ALT DIFFERENTIAL AND THE ACFT INSIDE THE 2.5 MI RING. I VISUALLY ACQUIRED THE CESSNA AT 9:30 - 10:00 POS INSIDE OF A MI; CO-ALT. ONCE CLR; RA COMMAND SYMBOLOGY TO RESUME CLB. COPLT IMMEDIATELY ASKED BOSTON DEP IF WE HAD MISSED ANY CALLS DUE TO THE ACTIVITY LEVEL AND DIVERTED ATTN GIVEN TO THE TCASII RA. DEP CTL RESPONDED BY SAYING THEY HAD GIVEN US A TA EARLIER ABOUT THE CESSNA. WE WERE THEN GIVEN A FREQ CHANGE TO NEXT ALT SECTOR. I ASKED FOR A PHONE NUMBER TO REACH THEM WHEN I ARRIVED AT DEST. NEXT SECTOR ADVISED THAT DEP WAS CONDUCTING SOME TRAINING AT THE TIME AND THEN RELAYED THE BOSTON DEP CTL PHONE NUMBER. NEITHER MYSELF NOR COPLT HEARD A TA. NEITHER MYSELF NOR COPLT ACKNOWLEDGED A CONFLICT TO ATC. DEP CTL WAS VERY BUSY AND ANY XMISSION FROM ATC TO US ABOUT A CONFLICT MAY HAVE BEEN BLOCKED. WE WERE OFF THE SID (WHYBE) AND ON AN ATC VECTOR AND CLBED TOWARDS A VFR/IFR CONFLICTING ACFT WITH NO FURTHER ADVISORIES OR WARNINGS OR QUERIES ABOUT OUR ACKNOWLEDGEMENT (OR LACK THERE OF). SHORT STORY: TCASII SAVED 150 LIVES. RA MANEUVER WAS ABRUPT IN PITCH AXIS AND MORE TEMPERED IN ROLL PLANE DUE TO UNKNOWN WHEREABOUTS OR CONFLICT ACFT. QUESTIONS: 1) TRAINING ON DEP CTL DURING BUSY TIME. 2) SUPERVISORY MONITORING TO AVOID INCIDENT. 3) FREQ -- TOO MUCH GOING ON. 4) ATC SITUATIONAL AWARENESS; VIS-A-VIS VECTOR AND CLB OFF A SID WITH POTENTIAL TFC CONFLICT AND NO FURTHER ADVISORY HELP. 5) SIZE AND BREADTH OF CLASS B AND LOGAN SUFFICIENT TO ACCOMMODATE TFC.