Usually, the O2 analyzer on the anesthesia machine samples at the CO2 absorber and is slower to respond.  Because of sampling location and slow response time, it cannot distinguish between inspired and expired O2.
 
The O2 analyzer that aspirates gas at the Y-piece exhibits a faster response time and can thus discriminate between inspired and end-tidal O2 (ETO2).  If both O2 analyzers are present, the faster response one is the one that should be used to determine the end-point of preoxygenation (denitrogenation) based on ETO2 reaching a given threshold.  
 
In my experience both types of O2 analyzers will reach the same value given enough time, that is they are equally accurate but one is much slower than the other.    
 
The fast O2 analyzer that samples at the Y-piece is usually self-calibrating (e.g., the Datex Ultima).  The slower O2 analyzer that comes with the anesthesia machine needs manual calibration from time to time.  
 
Therefore, for documentation purposes, especially in situations where the O2 value is changing fast or if you are not sure whether the analyzer has been calibrated, it would seem that the inspired O2 value displayed by the fast O2 analyzer should be the one recorded.
 
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