First thing I would do is check the Spark plugs and replace the Spark plug caps.You can chop a little of the HT cables back to get new metal to screw into.
See this thread for cheaper than OEM caps,
http://forums.sv650.org/showthread.p...hlight=SD05FMR
I'm also a great believer in fuel cleaners like Redex for keeping lines and carbs/fuel bodies clean
Wilkos Supermarkets are doing the 4 bottle deal again for £8.50.Last you ages.
Then give the bike a good run out.
Also search for info on,"SV650 Choke Plungers" as these sticking is a common cause of this kind of problem.
HTH