Your stock black is the sensor signal wire, the connection of the two
whites don't matter as they provide a path in and out (12V and ground) to
the O2 sensor's heater...the heater works either way.

To confirm your new sensor wiring you can try this:

http://home.flash.net/~lorint/lorin/fuel/oxybench.htm

Logically, blue is your new sensor's signal wire...if it was otherwise, no
one would be able to figure out which of the two blacks was signal.  While
you're splicing you may want to consider this:

http://my.tbaytel.net/guskers/gauges.html

The $20 gauge tells you a great deal about the state of your engine
management system.  In our cold (0 to -25F) weather I was very surprised at
how long the engine stays in closed loop operation.  It certainly gives you
a good indication of why fuel mileage drops so severely in cold weather
short hauls.