C172 AND TWIN CESSNA WERE REQUIRED TO TAKE EVASIVE ACTION TO AVOID A COLLISION IN TOL CLASS E AIRSPACE.

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I WAS ON A VFR FLT FROM LUK TO ONZ; CRUISING AT 7500 FT. I WAS USING VFR FLT FOLLOWING; TALKING TO TOL APCH. I ENCOUNTERED A BAND OF SCATTERED CLOUDS WITH TOPS APPROX 7000 FT. ADVISED CTLR I WAS CLBING TEMPORARILY TO 8500 FT TO MAINTAIN VFR CLOUD CLRNC. CTLR ACKNOWLEDGED. ARRIVING AT 8500 FT; I REALIZED THE BAND WAS WIDER THAN I FIRST THOUGHT (APPROX 30 MI) SO I DECIDED TO CLB TO 9500 FT. I ADVISED CTLR OF MY INTENTIONS. HE ACKNOWLEDGED. SOON THEREAFTER; HE ADVISED ME OF 'TFC 9000 FT; 5 MI NW; EBOUND.' I LOOKED; BUT SAW NOTHING AT THAT TIME. I LEVELED OFF AT 8700 FT UNTIL I COULD SEE THE OTHER ACFT. CTLR TOLD ME TO SWITCH FROM 126.1 TO 134.35 (OR VICE VERSA -- CAN'T TELL FROM MY SCRAWLED NOTES). BEFORE I COULD CHANGE FREQ; A FEMALE CTLR ADVISED 'TFC 2 MI NW EBOUND 9000 FT.' SHE ASKED MY INTENDED ALT. I REPLIED 9500 FT. SHE SAID 'CLB APPROVED' (OR SO I THOUGHT). AS I CLBED THROUGH 9000 FT; I SAW THE TWIN CESSNA AT 10 O'CLOCK POS LESS THAN 1/4 MI (HIDDEN BEHIND A DOOR POST). WE BOTH TOOK EVASIVE ACTION. HE PASSED IN FRONT OF ME LESS THAN 1000 FT. I FELT BUFFETING AS I PASSED THROUGH IS WAKE. AFTERWARD; I SWITCHED TO THE NEW FREQ. CTLR ASKED IF I HAD SEEN THE TWIN CESSNA. I REPLIED 'YES SIR; I DID.' FACTORS POSSIBLY CONTRIBUTING TO INCIDENT: 1) CHANGE IN CTLRS NEAR THE TIME OF THE INCIDENT (FIRST ADVISORY FROM A MALE; SECOND FROM A FEMALE). 2) NEARNESS TO A SECTOR BOUNDARY. (I'M ASSUMING THIS BECAUSE I HAD JUST BEEN GIVEN A NEW FREQ. ALSO; I DID NOT HEAR CTLR GIVE ANY ADVISORIES TO THE TWIN CESSNA. I ASSUME HE WAS ON THE FREQ I WAS SWITCHING TO.) 3) I MAY HAVE MISHEARD FEMALE CTLR SAYING 'CLB TO 9500 FT APPROVED.' 4) MY RELATIVE INEXPERIENCE. I SHOULD HAVE STAYED LEVEL AT 8700 FT UNTIL A) I SAW THE CONFLICTING ACFT; OR B) CTLR RPTED 'TFC NOT A FACTOR.' TO PREVENT A RECURRENCE: 1) BOTH PLTS SHOULD EXERCISE BETTER SEE AND AVOID TECHNIQUE. 2) CTLRS SHOULD HAVE VECTORED US AWAY FROM EACH OTHER INSTEAD OF MERELY GIVING ADVISORIES. 3) SPECIAL ATTN TO SHIFT CHANGES AND POTENTIAL CONFLICTS NEAR SECTOR BOUNDARIES.