Just to add on to the excellent points already made, it is important to be aware of the different configuration options in use on your existing Catalyst switches and ensure that you've prepared the equivalent on your new Meraki switches. A few that would be worth considering are:
Spanning Tree (as mentioned)
Link Aggregations
Access Control Lists (please note that there is a single ACL list which affects all switches in the network)
SFP Usage (make sure you are using certified Cisco Meraki parts to ensure functionality)
There are a lot of other documents which may be useful depending on your setup, so please have a look through the documentation site and see what configuration update you can make on the dashboard ahead of swapping out your devices. If there are any specific questions, let us know and we can do our best to help out
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