Which o2 sensor to change for codes p0420 in 2005 mazda 3 where the catalyst is missing

SOURCE: Location O2 sensor after cat for Mazda Miata 2002

Just had BOTH of my O2 sensors replaced in my 2002 Miata.  The sensors are located
1. at the back of the engine compartment look down (on the passenger side ) You should see a spark plug looking device near the bottom of the engine (on the side) it has a short wire output that goes to a connector looking device on the other end. This O2 sensor had a short wire connector on the other end
Probably can be replaced from the top.
2.  This one is tougher --- From underneath the vehicle just after the catalytic converter  you should be able to see the Spark plug like O2 sensor .  The person who repaired it for me had to trace the wire from the O2 sensor.  It goes up into ( perhaps the frame or bottom of the vehicle INTO the Driver compartment under the drivers seat.  It is located near the Center Console  right at the carpet seam. It was about in a straight line from the BACK of the Drivers side Car Door.  He felt around -- and located the Connector (under the carpet near the center console. .  He checked underneath the car to the point where the wire disappeared --to confirm he had the correct wire.  
Once he located where the sensor wire led to --He had the old sensor out and wire connector disconnected and a  New sensor and the connector installed in about 10 minutes.  
The O2 sensor for this one was much longer than the first O2 sensor in the engine compartment He had to use some sort of standard release spray on the old sensor itself --to remove the old O2 Sensor.   Since it is exposed to the elements under the car.   Wrench, I think a screwdriver  and the spray were all the tools I remember him using.....

The autozone code indicated only the engine compartment sensor was bad.
The repair man told me Both usually go bad at the same time.  
I fixed the first one only -- turned out the warning light lit up a day or so later indicating the second O2 Sensor under the vehicle was bad.  Fixed that as well -- have had no problems since -- repair was about 4 months ago.....

SOURCE: have a code po 430 catalyst efficiency below

You def have a catayst problem. Before changing the converter i would recommend changing both up and down stream oxygen sensor on bank 2. If they are old thats what the computer determines if the catalyst is good or not. Most of the time after changing the sensors and resetting the light the problem is solved.

SOURCE: Code P0133-02 (o2 sensor slow

just because you have a slow response code does not mean that you have a bad sensor, the slow response code is just telling you that the fuel system is very slow to respond to fuel delivery changes, this could be caused by many different things it could be as simple as the oil is contaminated with fuel, it could also be a problem with the fuel pressure, could also be a vacuum leak. the fact that you keep getting the same code with different sensors tells me that the problem is not the sensor but the fuel injection system. there is a flow chart for the fuel system and i am afraid you are going to have to have someone run a diag. check on the fuel system.....SORRY