LO Calc has built-in functions for that equivalent to Excel's audit functions. In Calc, it's called Detective, and is available from the Tools tab of the menu. Tracing precedents and dependents also have keyboard shortcuts, which are shown in the Detective menu.
Shift-f5 will place arrows from the current cell to all cells with formulas that reference that cell.
BTW, while they aren't 100% compatible as far as nuances of how a few functions operate (and macros), Excel can open Calc spreadsheets (.ods and other formats), and Calc can open Excel spreadsheets (.xls, .xlsx, and others), you generally don't need to use the original app. The precedent/dependant tracing functions are features of the spreadsheet software, they aren't specific to the spreadsheet. So if you normally use Excel and received a Calc spreadsheet, you can open it in Excel and use the Audit features. If you normally use Calc and receive either a Calc or Excel file, you can open it in Calc and use the Detective features.