This is taken care of by the Cross-Tie, so most people won't need to worry about this.
Anno 2070 isn't compatible with the Performance Enhanced Graphics option that is available in newer versions of CrossOver. Right click on the name of the bottle in your list of bottles, select Settings and make sure that Performance Enhanced Graphics isn't ticked.
When I had Performance Enhanced Graphics turned on, I would get graphical corruption in the form of strange vertical lines that appeared to come from random graphics assets. This corruption would disappear when I moved the game window, or used a scroll bar. It was also somewhat intermittent on the main menu, but was persistent once I entered a submenu.
I run CrossOver on macOS Sierra and Performance Enhanced Graphics may well work with Anno 2070 on other platforms such as Linux.
