Yes, Vyte can automatically detect and convert timezones, therefore, Vyte can share the availability of two teammates from different timezone on the same booking page.
Vyte automatically converts the common availabilities of both co-hosts (teammates that will be handling the meeting) to the timezone of the person booking the meeting.
Therefore, you won't have to worry that meetings will be booked when one of the team members is unavailable because of a timezone mix-up!