An equally good reply - thanks. There is one point I would like to stress, because I think you may have overlooked it: the blockchain does show all trades that took place, but it does not show the ones that didn't! Buy and sell walls don't appear on the blockchain, so there is not necessarily any record of the means used to steer the price once those walls have been removed.
The walls are not simple and they are not always just "a wall". You normally have one large wall and several smaller ones closer to the trading price to do the fine tuning. I've also often seen staggered walls: large fixed amount buys (e.g. 50 BTC each) staggered at 20 or 50 USD intervals to stack up the buy or sell side of the order books. I've seen it done one sided and I've seen it steered from both a buy and sell side at once. I've also seen it quickly alternated between the two.
Despite comments to the contrary, I have watched this in action many times for hours at a time (yes, I know, mundane things fascinate me), there is no doubt in my mind that BTC price is often manipulated through the orderbooks. It may also be done elsewhere too, I choose the orderbooks because they are clearly visible, but it does happen. Often. The fact that it could also happen with stocks does not negate the fact that it happens with BTC.
I call it "manipulation" because it is only semi-visible, and even then only to those who are alert and who know what to look for. It is also only carried out by the exceptionally wealthy who have a few thousand BTC available to steer the markets with. This puts it beyond the reach of the ordinary trader, who becomes a pawn to be exploited by the fat cats. They scare him, they psych him out, they outlast his staying power. They force him into a bad trade and then they gain the wealth that he lost. They manipulate the hell out of the traders in general, which is why I call this spade a spade.
The prize is calculated as the equilibrium of the top 20 exchanges by volume. Just throwing in a 1000 BTC bid or ask on one or even five exchanges at the same time does not change or manipulate the price whatsoever.
To have the price of BTC jump a few thousand Points in a short amount of time, you would need to throw in market orders like 30-60 Billion $ spread across the top exchanges, accepting any ask price... That would be manipulation.