While filling liquid oxygen into a tank, why do they do open one end?
The end is opened to allow oxygen gas to escape. The flow of liquid oxygen into the tanker will not be pumped, just undergoing the natural tendency to flow from an area of high pressure to low pressure. As such, there would come a point when the residual gas in the tanker would start to provide back pressure on the flow input, slowing it down &amp; potentially stopping it once pressures equalize between the tanker and the source. 

By allowing oxygen gas to escape the tanker, the pressure will always be lower in the tanker, and the flow will be faster more adequately fill the tanker. The same technique is used when topping up liquid nitrogen in an NMR spectrometer, for example.