Vitali-Sanders Wlad-Peter 1 Wlad-Brewster 2 Vitali-Peter Haye-Valuev Wlad-Haye Vitali-Chisora Wlad-Povetkin Wlad-Pulev Fury-Wlad
It wasn't the easiest 10 fights to compile, the only fights that got in automatically for me were Vitali-Sanders (start of the era, "avenging" Wlad), Wlad-Peter 1 (underdog win, life and death, revival of Wlad's career), Wlad-Haye (close odds, superfight between two Ring champions, 10th consecutive defence, Klitschko bros capture all of the belts) and Fury-Wlad (wide underdog win, end of the era and a historically long title reign, passing of the torch). I considered Brewster's WBO title fights against Golota and Liakhovich, Fury's fights against Chisora 1 and Cunningham and Wlad-Byrd 2.
The approximate duration to define the Klitschko era would be from 2006 to 2015, roughly 9 and a half years. Vitali won the belt in 2003, made two defense and sailed off into the sunset until his fight with Peter. Wlad was losing fights in the mid 2000's, and it wasn't until the second Byrd fight where everything came in motion - the start of Wlad's peak and the return of Vitali is the proper start for their dominance IMO. The 10 most important fights I guess. Wlad vs Byrd II, Wlad vs Ibragimov, Vitali vs Peter, Wlad vs Chagaev, Vitali vs Solis, Wlad vs Haye, Vitali vs Adamek, Wlad vs Povetkin, Wlad vs Pulev, Wlad vs Fury.
I don't agree with that duration, I'd say 2004-2015 is most accurate (I believe that's generally accepted). Vitali won the WBC belt in 2004 (not 2003) when he beat Sanders and "avenged" Wlad, he was seen as the No.1 of the titlists at that point and was awarded the Ring title. Wlad also didn't lose from that point on for 11.5 years and was considered the best in the division (with Vitali's 2005 retirement) after he beat Peter 1 in 2005. Vitali didn't return until 2008 and had his final fight in 2012. The Klitschko's were a combined 6-0 in their last 6 fights when Wlad fought Byrd for a second time in 2006.
Lewis Vs. Vitali is the No.1 heavyweight in the 21st century. It's bigger than Fury-Wlad, Fury-Wilder, Haye-Valuev, ...or any other fight. In 1999, Vitali won the WBO title by beating Herbie Hide. Defended the title 2 times. Lost by injury to Chris Byrd. In the next fight, Wladimir Klitschko beat Chris Byrd in 2000; won the WBO title, and defended it 5 times. He was then knocked out by Corrie Sanders. If it's the Pre-Klitschko era, that's ok.
"Lewis Vs. Vitali is the No.1 heavyweight in the 21st century" It depends on the metric; it wasn't the most lucrative, it wasn't a big upset (or an upset at all: Lewis was a 1/5 favourite), it wasn't statistically unique, or a passing of the torch (as Fury-Wlad was). And it certainly wasn't the Klitschko era! Vitali lost to Byrd in 2000, lost to Lewis in 2003, Wlad lost to Sanders months prior, lost to Brewster early 2004. Vitali was on a 5-2 run, Wlad was in the midst of a 2-2 run. How can it be the Klitschko era if 1. a non-Klitschko was the recognised champion 2. the Klitschko's were not in consistent winning form? They were the dominant force from Vitali-Sanders on: a combined 34-0 with 24 KO's from 24th April 2004 until November 2015. 2003 was still Lewis's era, which started when he became undisputed in 1999.