How does that affect performance and the Velocity stacks are engineered to mix the air and fuel so Let me know what that did to your Ducatti and why would you do that to a awesome bike like that?
These "velocity stacks" are before the filter, so there is no fuel mixing going on. Fuel comes in much later. These snorkels are mainly there for noise abatement, creating a disturbance in the airflow so that there is no "drone" from the intake. You could just remove them and then the only limiting factor for intake volume is the size of the holes they were in. So removing the cover that contains those holes exposes the entire filter element to fresh air, thus providing a great deal more air for the engine to inhale. However, you also create more sucking sound and hum from the intake, so there are tradeoffs.
It looks to me that you can't actually remove the lid on this intake, as it is more integral to the entire box. On my Duc, the filter is horizontal and a lid is placed on top of it with two small snorkels on it. Removing the whole shebang is the way to go. In fact, the Ducati Performance intake/computer/exhaust kit comes with a 1/4" wide retaining ring to hold the air filter on, eliminating the whole box top, snorkels and all.
So anyway, I think you ought to remove the snorkels and cut the material between the holes, creating one large hole for the air to enter the box. As it is, or as it has been modified here, you're still only getting a small portion of the air filter exposed to fresh air. Me, I'm quite happy with the bike as it is.