Volume Meassurement (Dry Method)

Referring to the operation I can't find a convincing explanation for these 2 facts:

-The spike in the curve right when inflation finishes.
-The slight difference during the first half of deflation between the ideal exponential decay curve (pink) and the real pressure measured (top of the blue area). After that they are almost identical.

These are factors I've been weighing in to find answers:

-I'm using elastic (very flexible) silicone tubing which expands and contracts.
-Leaks in the system dependent on pressure, adding weight to the exponential decay at the beginning of deflation when the pressure is higher.
-The fact that air is a compressible fluid.
-Reduction in hose diameter to connect to the Pr. sensor.
-Delays in the transmission of the pressure waves inside the pneumatic system.
-Minute decreases in air temp as it enters the container and expands.
-The fact that I'm using a one piston compressor directly driving the pressure in the system and not from a stable pressure source such as a tank and inflating though a solenoid valve openning .
-The whole theory is wrong and I made too many approximations and assumed too many equivalences.

Even when these 2 facts appear to be constant and therefore systematic and the way I'm calculating the volume apparently effectively cancels them, it will be good to find answers to these questions.
Any ideas??
Thanks