Measured continuity between live and neutral
Measuring continuity on a circuit can be a false measurement.

A multi-meter tests continuity by measuring if a certain amount of DC current flows from the Positive to the Common terminal.
On a wire, with low resistance, this current will flow without a problem.   

However components like a capacitor or transformers can also act as a wire for the DC test current of the meter.
A capacitor will allow the DC test current to charge it.
A transformer looks like a resistor for a DC test current.  

If the capacitor is small, it will beep shortly and the resistance will quickly rise. The capacitor is charged. But if you have a large capacitor, the meter might not be able to charge it, and read as a short circuit for a DC continuity test.

Measuring continuity on the Live and Neutral or Positive and Negative of a device might not provide the result you expect.